Physics quiz question: comparing horizontal velocity components

Physics 205A Quiz 3, fall semester 2019
Cuesta College, San Luis Obispo, CA

Two velocity vectors shown at right have different speeds and directions. All angles are measured counterclockwise from the +x axis. Velocity vector __________ has the larger horizontal component magnitude.
(A) v_A.
(B) v_B.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (B)

Since these θ angles are measured counterclockwise from the +x axis, the horizontal components of these velocity vectors are given by:

v_A,x = v_A·cosθ_A,
v_B,x = v_B·cosθ_B.

Then the horizontal components are these velocity vectors can be calculated and compared:

v_A,x = v_A·cosθ_A = (10 m/s)·cos(80°) = 1.736481776669303... m/s,

or to two significant figures, the horizontal component of v_A has a magnitude of 1.7 m/s, while:

v_B,x = v_B·cosθ_B = (4.0 m/s)·cos(60°) = 2.0 m/s.

Thus the horizontal component of v_B is greater than the horizontal component of the horizontal component of v_A.

Sections 70854, 70855
Exam code: quiz03Ch3V
(A) : 4 students
(B) : 49 students
(C) : 1 student
(D) : 0 students

Success level: 91%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.19

Online reading assignment: projectile motion

Physics 205A, fall semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on projectile motion and forces/interactions.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"I understand that the horizontal component of projectile motion is constant when we disregard air resistance, but the vertical component changes because of gravity. I also understood the concept of the 'range' as being the horizontal distance traveled between launching and landing, assuming that the projectile returns to the same vertical level that it was fired at."

"Our approach to solving projectile motion problems will be to separate the horizontal motion and vertical motion parts of the problem and solve them separately. For the vertical motion, we will use the kinematic equations and rules of free fall. For the horizontal motion, we will use the kinematic equations for constant acceleration problems."

"After doing the assigned reading I learned that projectile motion depends on two independent ingredients: vertical (free fall motion) and horizontal (constant velocity motion). I also learned that vertical motion is described with the same set of free fall equations that we have seen before."

"I am slowly starting to understand where the symbols go to. Making a drawing for a problem that has a lot of information helps a lot, more than I thought."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"Something that I found confusing is when trying to find two variables and which equation to use if you are trying to find two variables."

"I just need more practice with the different types of formulas."

"I didn't quite understand the explanation on how to apply the equations to the word problems."

"I am still struggling with trying to remember just little things like some of the symbols. And trying to find out the information that's giving but is not useful."

Indicate the initial velocity components for the (ideally) vertically-launched anvil. Choose up to be the +y direction.
(Only correct responses shown.)

v_0x: 0 [74%]
v_0y: positive [60%]

(The initial velocity (as the anvil is launched) is vertical, with no horizontal components.)

Indicate the acceleration components after the anvil was launched. Choose up to be the +y direction.
(Only correct responses shown.)

a_x: 0 [70%]
a_y: negative [51%]

(Neglecting air resistance, the only force acting on the the anvil after it was launched is due to gravity, such that there is a vertical acceleration (–9.80 m/s², the negative denoting that it acts downwards). And since there are no forces acting horizontally to change the (zero) horizontal motion of the anvil, the horizontal acceleration is zero.)


Indicate the initial velocity components for the car driven horizontally off the cliff. Choose right to be the +x direction, and up to be the +y direction.
(Only correct responses shown.)

v_0x: positive [81%]
v_0y: 0 [47%]

(The initial velocity (as the car leaves the cliff) is horizontal, with no vertical component.)

Indicate the acceleration components after the car was driven horizontally off the cliff. Choose right to be the +x direction, and up to be the +y direction.
(Only correct responses shown.)

a_x: 0 [37%]
a_y: negative [60%]

(Neglecting air resistance, the only force acting on the the car after it was driven off the cliff is due to gravity, such that there is a vertical acceleration (–9.80 m/s², the negative denoting that it acts downwards). And since there are no forces acting horizontally to change the (constant) horizontal motion of the car, the horizontal acceleration is zero.)


Indicate the initial velocity components for the car launched diagonally off the cliff. Choose right to be the +x direction, and up to be the +y direction.
(Only correct responses shown.)

v_0x: positive [72%]
v_0y: positive [64%]

(The initial velocity (as the car leaves the ramp) is diagonally upwards, with a positive (upwards) vertical component, and a positive (rightwards) horizontal component. Note that the the launch angle θ will have some value between 0° and 90°, in the first quadrant of the unit circle (as measured counterclockwise from the +x direction).)

Indicate the acceleration components after the car was launched diagonally off the cliff. Choose right to be the +x direction, and up to be the +y direction.
(Only correct responses shown.)

a_x: 0 [32%]
a_y: negative [58%]

(Neglecting air resistance, the only force acting on the the car after it was launched off the ramp is due to gravity, such that there is a vertical acceleration (–9.80 m/s², the negative denoting that it acts downwards). And since there are no forces acting horizontally to change the (constant) horizontal motion of the car, the horizontal acceleration is zero.)

Describe a situation with a negative starting angle of elevation θ for projectile motion.

"When shooting a bullet downwards from the edge of a cliff."

"Throwing a rock down into a chasm."

"A cannon on top of a cliff is pointed at a downward angle θ from the horizontal at some initial velocity."

"A kid accidentally kicks his soccer ball to the roof of his house. Not wanting to make his parents mad, he climbs to the roof and finds the ball, then places it on the roof and kicks it off at a negative angle of elevation θ."

"A car rolling backwards down a hill (and off of a cliff)."

"I really have no idea."

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Hope you had an awesome three day weekend." (I did, thank you for asking. Hope yours was awesome as well.)

"I really need to refresh my memory of the terminology as far as the subscripts, like v₀ and whatnot." (That's okay, it's probably because you had an awesome three-day weekend.)

"Will Quiz 2 cover everything that we have done after the first quiz?" (Yes, but only up until free fall--so essentially constant acceleration motion that is either only horizontal, or only vertical. Quiz 3 will cover constant acceleration motion that is both horizontal and vertical (that is, projectile motion), and also forces and Newton's laws.)

"Are we supposed to memorize the equations that are given in this assigned reading assignment?" (No. All relevant equations are always given to you for the quizzes and exams.)

"Is air resistance always going to be ignored in these problems?" (For the purposes of this course, we will always neglect air resistance.)

"Will there ever be situations or problems where we will be starting to take air resistance into consideration?" (Only if you decide to major in physics.)

"When it comes to acceleration, is it always zero in the horizontal direction?" (Yes, because the horizontal velocity must stay constant if there is no air resistance.)

"I feel like I need to brush up on my trigonometry, it feels like it has been a while since I've worked with it."

"Are we going to use Excel again? (You will be using Excel for nearly every lab, except for when we use motion tracking software to analyze slow-motion videos and generate velocity versus time graphs.)

"Will we be working on any launch velocities and accelerations in lab? It would be helpful to be able to see this in person to visualize it better. (The next lab will have you using motion tracking software to analyze slow-motion videos of projectile motion.)

"I am slightly confused by the initial velocity for when a car is launched horizontally. I think that the car would have a (a) positive initial velocity for the x-direction, and a (b) negative initial velocity for the y-direction, but I'm looking forward to lecture to see if my assumption is true." (We'll cover this with an example in class, but: (a) yes; (b) no.)

"Please make sense of the examples and how to do the calculations with setup and finding solutions in hands-on problems to make the connections of how to complete the work." (Yes.)

"Parabolas make me think of quadratic equations, which makes me think about possibly getting to use the quadratic formula. I'm excited for the opportunity to refresh my mind on that!" (Be careful for what you wish for.)

"I'm really hoping I pass this class." (I hope so, too.)

Physics quiz question: soccer ball horizontal velocity component

Physics 205A Quiz 3, fall semester 2018
Cuesta College, San Luis Obispo, CA

A Physics 205A student kicks a soccer ball such 
that it has an initial speed of 21 m/s, with an angle of 155°, as measured counterclockwise from the +x direction. Neglect air resistance. The horizontal component of the soccer ball's initial velocity vector is:
(A) –19 m/s.
(B) –8.8 m/s.
(C) +8.8 m/s.
(D) +19 m/s.

Correct answer (highlight to unhide): (A)

The initial velocity vector of the soccer ball is at an angle of 155° as measured counterclockwise from the +x axis (i.e., the "unit circle angle"). Using this θ = 155° angle allows the ± signs in the initial velocity vector components to naturally result from the calculations:

v_0x = v₀·cosθ,
v_0y = v₀·sinθ.

Then the horizontal component of the initial velocity vector is then:

v_0x = v₀·cosθ,

v_0x = (21 m/s)·cos(155°) = –19.032463527769649 m/s,

or to two significant figures, v_0y = –19 m/s.

(Response (D) is the initial horizontal speed, but directed to the right; response (C) is the vertical component of the initial velocity vector (21 m/s)·sin(155°); response (D) is the initial vertical speed, but directed downwards.)

Sections 70854, 70855
Exam code: quiz03pRH5
(A) : 42 students
(B) : 5 students
(C) : 3 students
(D) : 6 students

Success level: 75%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.60

Online reading assignment: projectile motion, identification of forces

Physics 205A, fall semester 2018
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on projectile motion and forces/interactions.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Projectile motion combines both vertical free fall and a constant horizontal velocity."

"In projectile motion you focus not so much on the horizontal motion but the vertical motion because it takes gravity into account."

"Projectile motion has both a vertical and horizontal component, although they are independent of each other."

"Projectile motion is merely vertical free fall, with an added horizontal velocity component."

"If something is launched diagonally, it means there is an initial horizontal and vertical velocity component."

"Adding horizontal velocity to a vertical free fall will still cause the object to fall at the same speed as if it had no horizontal velocity. The horizontal motion and free fall motion are independent of each other. Net force is the sum of all forces acting on an object and will depict the changing (or non-changing) movement of the object."

"The differences between mass and weight such that the weight of an object exists because of the objects gravitational pull towards earth and mass is a quantitative measure of inertia. Mass is an intrinsic property and weight van vary."

"The different forces and what they mean. There is weight force (the force of gravity), normal force (the force exerted by a surface), tension force (the force exerted along a string, rope, or cable), and there is static/kinetic force (the forces used to unstick or slide an object along a surface."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"Determining whether an object has zero or positive or negative initial velocity components in a specific direction is tough since it depends on the situation of a problem. If it's from rest it may be zero, however if the problem starts off with the ball in movement it's more difficult."

"The equations and variables. Would need typical example equations done in class."

"The trigonometry parts are still difficult for me."

"When and how to use the quadratic formula."

"I need a little help understanding how the force equations exactly work when more than one force is at work."

"I would like to know where the formulas are coming from."

"I am lost with the forces. Is weight a force? WHY?"

"I have a good amount understanding the new equations given to us and how to implement them algebraically into functions that I can solve. I'll mention this in class and personally seek help on the difficult ones."

"Nothing was particularly confusing, but it will take some practice to apply it all."

"I actually feel as though I understand this pretty well, I didn't feel as though there was one thing that was overwhelmingly confusing."

Indicate the initial velocity components for the (ideally) vertically-launched anvil.
(Only correct responses shown.)

v_0x: 0 [73%]
v_0y: positive [51%]

(The initial velocity (as the anvil is launched) is vertical, with no horizontal components. This makes the launch angle θ = 90° (as measured counterclockwise from the +x direction).)

Indicate the acceleration components after the anvil was launched.
(Only correct responses shown.)

a_x: 0 [47%]
a_y: negative [43%]

(Neglecting air resistance, the only force acting on the the anvil after it was launched is due to gravity, such that there is a vertical acceleration (–9.80 m/s², the negative denoting that it acts downwards). And since there are no forces acting horizontally to change the (zero) horizontal motion of the anvil, the horizontal acceleration is zero.)


Indicate the initial velocity components for the car driven horizontally off the cliff.
(Only correct responses shown.)

v_0x: positive [65%]
v_0y: 0 [43%]

(The initial velocity (as the car leaves the cliff) is horizontal, with no vertical component. This makes the launch angle θ = 0° (as measured counterclockwise from the +x direction).)

Indicate the acceleration components after the car was driven horizontally off the cliff.
(Only correct responses shown.)

a_x: 0 [20%]
a_y: negative [74%]

(Neglecting air resistance, the only force acting on the the car after it was driven off the cliff is due to gravity, such that there is a vertical acceleration (–9.80 m/s², the negative denoting that it acts downwards). And since there are no forces acting horizontally to change the (constant) horizontal motion of the car, the horizontal acceleration is zero.)


Indicate the initial velocity components for the car launched diagonally off the cliff.
(Only correct responses shown.)

v_0x: positive [78%]
v_0y: positive [59%]

(The initial velocity (as the car leaves the ramp) is diagonally upwards, with a positive (upwards) vertical component, and a positive (rightwards) horizontal component. Note that the the launch angle θ will have some value between 0° and 90°, in the first quadrant of the unit circle (as measured counterclockwise from the +x direction).)

Indicate the acceleration components after the car was launched diagonally off the cliff.
(Only correct responses shown.)

a_x: 0 [27%]
a_y: negative [63%]

(Neglecting air resistance, the only force acting on the the car after it was launched off the ramp is due to gravity, such that there is a vertical acceleration (–9.80 m/s², the negative denoting that it acts downwards). And since there are no forces acting horizontally to change the (constant) horizontal motion of the car, the horizontal acceleration is zero.)

Describe a situation with a negative starting angle of elevation θ for projectile motion.

"We are rolling a marble down a ramp that ends at the edge of a table. Projectile motion begins after the marble leaves the ramp."

"If a car is driven off a cliff that originally sloped downwards."

"Throwing something downward off the top of a building."

"Kicking a ball of a cliff downward as opposed to kicking it upwards."

"Somebody throws a football down at a person from a roof top."

"I don't know."

"What?"

Identify the type of interaction ("force") with its symbol. (Only correct responses shown.)

Weight ("gravitational force") : w [90%]
Surface contact force ("normal force"): N (or F_N) [82%]
Tension ("rope/cable/string force"): T [90%]
Kinetic friction ("sliding force," or "sliption"): f_k [86%]
Static friction ("sticking force," or "stiction"): f_s [82%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"One of the things that I don't quite understand is the concept of a projectile aving a constant horizontal motion. Does that mean that the horizontal acceleration is zero? I just don't see how a projectile has a constant horizontal motion." (If air resistance is negligible, then after the projectile is launched, there is nothing to slow down or speed up its horizontal motion. However, after the projectile is launched, there is still the force of gravity that acts on it to cause a vertical acceleration.)

"Horizontal acceleration is zero because we neglect air resistance?" (Yes.)

"Horizontal velocity remaining constant if there is no air resistance?" Wouldn't the object eventually slow down or would that be caused by a different factor?" (Realistically, yes, an object would eventually slow down horizontally because of air resistance; but since we'll be neglecting it for the purposes of this class (which may or may not necessarily be a reasonable assumption), then for this idealized case the horizontal motion will remain constant.)

"If a vertical launch has no horizontal motion, then we can ignore the horizontal component of velocity and acceleration, right? (Yes.)

"Could you please clarify the initial velocity and acceleration components in class, please?" (Part of the next reading assignment is to review those launch examples again, but with specific comments on how to deduce those horizontal and vertical components for velocity and acceleration.)

"The use of the quadratic equation was thrown in on the presentation preview but didn't really explain how we use it. Hopefully there will be clarification in class?" (There will be. But it won't be pretty.)

"I did not understand free-body diagrams. Can all of the forces be added into a free-body diagram amongst each other?" (There can be. But it won't be pretty.)

"Will we have to memorize any of the equations, or will they be given to us on a quiz?" (All necessary equations will be given on a quiz. The only "equations" not given on a quiz are definitions (such as trigonometry, etc.).)

Physics quiz question: direction of vector, given components

Physics 205A Quiz 3, fall semester 2017
Cuesta College, San Luis Obispo, CA

A vector R has x- and y-components as shown at right. The direction of vector R, as measured counterclockwise from the +x direction is:
(A) 103°.
(B) 167°.
(C) 193°.
(D) 257°.

Correct answer (highlight to unhide): (B)

Many calculators do not properly calculate the angle of a vector counterclockwise from the +x axis, instead calculating an angle θ for the related vector in the first quadrant (by dropping ± signs from the R_x and R_y components in the arctangent operation. Thus this "first quadrant angle" θ is:

θ = Arctan|R_y/R_x| = Arctan|(0.8 units)/(3.6 units)| = 13°.

However, since we know that the vector R must be in the second quadrant, then we will need to subtract this "first quadrant angle" θ from 180° such that the direction of R measured counterclockwise from the +x axis is:

180° – 13° = 167°.

For the cases of vectors in other quadrants, if the vector truly lies in the first quadrant, then its direction is the same as the "first quadrant angle" θ. If the vector lies in the second quadrant, then its direction is the "first quadrant angle" θ subtracted from 180°. If the vector lies in the fourth quadrant, then its direction is the "first quadrant angle" θ subtracted from 360°.

(Response (A) is 90° + 13°; response (C) is 180° + 13°; response (C) is 270° – 13°.)

Sections 70854, 70855
Exam code: quiz03T4uC
(A) : 9 students
(B) : 37 students
(C) : 5 students
(D) : 3 students

Success level: 69%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.63

Online reading assignment: projectile motion, identification of forces

Physics 205A, fall semester 2017
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on projectile motion and forces/interactions.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"I understand the basics and values of components in vertical, horizontal, and diagonal launches. Also the force interactions and their corresponding symbols."

"Gravity is a downward force that has an effect on a projectile's vertical motion. There is no horizontal force in a projectile motion, so it will have a constant horizontal velocity."

"When dealing with the vertical motion of an object you can use the same kinematic equations as the horizontal.However, when dealing with projectile motion you have to deal with both the vertical and horizontal motion."

"Everything is pretty much the same, same formulas just a little more added. We were doing one dimensions now we are doing two dimensions."

"A projectile is an object with only gravity as the force acting upon it. The trajectory is the path a projectile travels. Projectile motion depends on the independent horizontal and vertical motions. Trajectory motion is vertical free fall with horizontal constant added. Weight, normal, tension, static and kinetic are forces that can be described for an object through a free body diagram and when added together create net force."

"I understand the five kinematic equations and how to pick the one to solve, because the process of elimination is really easy, and I've dealt with it before."

"The perpendicular force of an object is the normal force being exerted. The magnitude of static frictional force is the coefficient of static force of a material multiplied by the magnitude of the normal force."

"I feel like I understand the individual forces themselves. They all play their own part in the mechanical aspects of reality in unique ways."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I still think that the sine and cosines are confusing but I feel I will get it the more we practice. Besides that I think it makes sense if I know what each variable means."

"One thing I struggled with is trigonometry. I sometimes forget which function to use for a particular situation."

"Just setting up the problems; I can't get the steps right to pick the right formula. I read the problem and just freeze on the setup."

"How to choose the more straightforward equation when solving a problem; I'm usually really slow so I would like to be more efficient and not waste too much time doing more work than I should but I'm always taking the long path."

"Projectile motion equations are confusing in general."

"The equations are confusing, but I think once applied and talked about will make more sense. Can you better describe 'normal force?'"

"The difference between kinetic and static friction. It seems to me that they are mostly the same with a slight difference but I am ultimately unsure."

"I did not find the material too confusing. Working through the problems can be a little difficult though."

"I didn't find anything confusing or did not remember anything confusing."

Indicate the initial velocity components for the (ideally) vertically-launched anvil.
(Only correct responses shown.)

v_0x: 0 [88%]
v_0y: positive [71%]

Indicate the acceleration components after the anvil was launched.
(Only correct responses shown.)

a_x: 0 [67%]
a_y: negative [44%]

Indicate the initial velocity components for the car driven horizontally off the cliff.
(Only correct responses shown.)

v_0x: positive [78%]
v_0y: 0 [56%]

Indicate the acceleration components after the car was driven horizontally off the cliff.
(Only correct responses shown.)

a_x: 0 [27%]
a_y: negative [75%]

Indicate the initial velocity components for the car launched diagonally off the cliff.
(Only correct responses shown.)

v_0x: positive [79%]
v_0y: positive [48%]

Indicate the acceleration components after the car was launched diagonally off the cliff.
(Only correct responses shown.)

a_x: 0 [21%]
a_y: negative [54%]

Describe a situation with a negative starting angle of elevation θ for projectile motion.

"A car going down a ramp which angle is in the fourth quadrant."

"Releasing a bowling ball into the bowling lane; it has a fast positive horizontal velocity component and slow negative vertical velocity component, creating a negative angle when it leaves your hand."

"A gun is fired from a building to the street below."

"I am unsure of an example and could benefit from going over this."

"I don't understand the question. If you could address it in class that would be much appreciated!"

"When the Night's Watch is shooting an arrow from the wall down to the wildlings." (#winteriscoming)

"When Frodo threw the ring down into Mt. Doom, the ring hag a negative starting angle of elevation heading into the fiery pit of evil." (Don't forget Gollum also fell with a negative starting angle of elevation into the depths of Mt. Doom. #somethingsthatshouldnothavebeenforgottenwerelost)

Identify the type of interaction ("force") with its symbol. (Only correct responses shown.)

Weight ("gravitational force") : w [81%]
Surface contact force ("normal force"): N (or F_N) [85%]
Tension ("rope/cable/string force"): T [94%]
Kinetic friction ("sliding force," or "sliption"): f_k [85%]
Static friction ("sticking force," or "stiction"): f_s [87%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Why do we take the square root of the sum of the squared horizontal components and vertical components to find a vector magnitude?" (Pythagorean theorem; the magnitude is the hypotenuse of a right triangle with the horizontal and vertical components as its sides.)

"I was wondering if there is an equation sheet we plug knowns and unknowns into like the past. Some of those formulas became very complex." (Yes, the horizontal and vertical kinematic equations will be given to you for the next quiz.)

The material seems easy, but the in-class approach can be confusing."

"I like how the process we go through to find givens, unknowns and what to solve for in the list of five."

"I would really like you to do more lecturing in class and less practice quizzes and worksheets."

"Possibly more review on projectile motion and being sure of which equation/which variables we want to solve for."

"Could we go over questions that use all of these variables in class?"

"Can you explain the angles and components a bit more in-depth or go over it with a few more examples? I feel like we didn't have enough time to get the idea in."

"Can we use the blog to find more related problems to practice on?" (I've pretty much linked to all the old quiz questions that are on the blog with worked-out solutions that are worth doing for homework. If you really to see all the quizzes posted from previous semesters (which don't all have answers given), then you can click on (or search for) the tag "physics quiz archive," and just keep scrolling down the page, backwards into time.)

"How useful is doing calculations in ideal situations when in real life air resistance gets in the way of things?" (Well, ignoring air resistance would get you numerical results that would only be approximately correct; but realistically bigger uncertainties would probably come from not being able to precisely measure the experimental direction and speed of the initial velocity vector, etc.)

"If we imagine that gravity doesn't exist on Earth and we launch something horizontally, would it keep going straight until it crashes on another object? But if there is no gravity in the space, why do shooting stars are falling?" ((1) Yes, if we could turn off gravity. (2) But Earth exerts gravity everywhere around it, even in space, so it can still pull in meteoroids (small rocky debris) into the atmosphere, where they'll burn up as meteors ("shooting stars"). Bonus fact: surviving fragments found on the ground are meteorites.)

"In an orbit, what do we consider our starting and ending points if the object is in continuous motion?" (For something like that, you would pick an arbitrary starting point, and then your ending point would be just a fraction of a second later from that, and analyze its change in motion. Then you would consider that your new starting point, and then your ending point would be just a fraction of a second later from that, so you would re-calculate its change in motion. And so on. So basically, this is essentially vector calculus, differentiating and integrating over time (step-by-step) over each part of the orbital path.)

"The 'launched diagonally' car was CGI, obviously."

"I really enjoy your positive attitude towards physics." (Let's see if I can maintain that for the next sixty semesters until I can retire from teaching. #sixtysemestersuntilretirement)

Physics quiz question: downwards-aimed BB pellet vertical component

Physics 205A Quiz 3, fall semester 2016
Cuesta College, San Luis Obispo, CA

A BB gun shoots a pellet with a speed of 105 m/s at an angle of 40° below the horizontal, down towards the ground below. Neglect air resistance. The initial vertical velocity component of the pellet was:
(A) –67 m/s.
(B) –80 m/s.
(C) –88 m/s.
(D) –1.4×10² m/s.

Correct answer (highlight to unhide): (A)

The initial velocity vector of the BB is 40° below the horizontal, which corresponds to an angle of θ = 360° – 40° = 320°, as measured counterclockwise from the +x axis (i.e., the "unit circle angle"). Using this θ = 320° angle allows the ± signs in the initial velocity vector components to naturally result from the calculations:

v_0x = v₀·cosθ,
v_0y = v₀·sinθ.

Then the vertical component of the initial velocity vector is then:

v_0y = v₀·sinθ,

v_0y = (105 m/s)·sin(320°) = –67.4926990171 m/s,

or to two significant figures, v_0y = –67 m/s.

(Response (B) is (105 m/s)·cos(320°); response (C) is (105 m/s)·tan(320°); response (D) is (105 m/s)/cos(320°).)

Sections 70854, 70855, 73320
Exam code: quiz03sHO7
(A) : 30 students
(B) : 19 students
(C) : 7 students
(D) : 1 student

Success level: 53%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.61

Online reading assignment: projectile motion, identification of forces

Physics 205A, fall semester 2016
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on projectile motion and forces/interactions.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"For projectile motion, vertical direction differs from horizontal direction as vertical direction has an acceleration due to gravity. If there is no air resistance, there is no horizontal acceleration (making it zero)."

"How projectile motion can be divided into two parts, the horizontal motion of the object and the vertical motion. It makes sense to me how the acceleration would be zero in the horizontal direction and how it would be –9.8 m/s² in the vertical direction."

"I am going to have a lot of questions tomorrow in class."

"I understand projectile motion and how it is the same as vertical free fall. However, it will have an added horizontal velocity. So, the ball and or object will be 'falling' but not in a straight line."

"Regarding projectile motion the initial horizontal and vertical velocity are considered individually. v_0x is the initial velocity on the horizontal axis and v_0y is the initial velocity on the vertical axis."

"Horizontal and vertical motions act independently. This means that the height reached by a bouncing ball is only dependent on the vertical velocity and height of its release, and not it's horizontal velocity."

"There are four different force types, weight, normal, tension/elastic, and friction. Each of these different forces can be calculated differently. Weight force is calculated by the mass times the graviational constant, the normal force which can vary from 0 to infinity depending on the surface exerting the force, and this is also true of a tension force, depending on the material. For the static friction force, it is also calculated the same by which can range form 0 up until it gets the object in motion."

"The different types of forces that were covered. There is gravitational force, normal force, static force, kinetic force, and tension force. These all have a way of affecting whether or not an object moves or how it stays in place."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I'm still not very good with when and how to use sin, cos, and tan. So going over that would be very helpful!"

"I think this section is much easier to understand once you know exactly which equation(s) to use. The more practice with determining which equation to use, will help with projectile problems."

"What I found confusing was when adding forces together how that would equal the net force, especially if those forces were working in different directions."

"I still struggle with reading the math and would benefit from practicing in class."

"The concept of projectile motion and trajectory. I am a visual learner so the pictures help, but I would still need to explanation on the x and y components of projectile motion."

"I don't think I quite understand how to do all the math of everything quite yet, but all of the equations on paper do make sense."

"Not too much--if you understand trigonometry, you're good."

Indicate the initial velocity components for the (ideally) vertically-launched anvil.
(Only correct responses shown.)

v_0x: 0 [76%]
v_0y: positive [56%]

Indicate the acceleration components for the (ideally) vertically-launched anvil.
(Only correct responses shown.)

a_x: 0 [69%]
a_y: negative [44%]

Indicate the initial velocity components for the car driven horizontally off the cliff.
(Only correct responses shown.)

v_0x: positive [73%]
v_0y: 0 [56%]

Indicate the acceleration components for the car driven horizontally off the cliff.
(Only correct responses shown.)

a_x: 0 [44%]
a_y: negative [60%]

Indicate the initial velocity components for the car launched diagonally off the cliff.
(Only correct responses shown.)

v_0x: positive [69%]
v_0y: positive [47%]

Indicate the acceleration components for the car launched diagonally off the cliff.
(Only correct responses shown.)

a_x: 0 [33%]
a_y: negative [47%]

Describe a situation with a negative starting angle of elevation θ for projectile motion.

"If you threw a rock from a cliff down towards the lake below, that would have a negative starting angle."

"If you stood on the edge of a roof and launched a projectile towards the street, it would be moving positively to the right and down."

"A marble rolling off a slanted drafting table."

"I can't. Going to need help."

"Cyclops (from X-Men) standing tall, looking down to blast a big rat on the floor. His high energy beam projects at a negative angle of elevation."

Identify the type of interaction ("force") with its symbol. (Only correct responses shown.)

Weight ("gravitational force") : w [80%]
Surface contact force ("normal force"): N (or F_N) [78%]
Tension ("rope/cable/string force"): T [89%]
Kinetic friction ("sliding force," or "sliption"): f_k [87%]
Static friction ("sticking force," or "stiction"): f_s [84%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"I like when you do examples on the board in class. They are extremely helpful."

"I found the horizontal component of acceleration slightly confusing. Is a_x always equal to zero for projectile motion when ignoring air resistance?" (Yes!)

"Were we supposed to neglect air resistance in the above examples?" (Yes.)

Physics quiz question: component of vector, given magnitude and other component

Physics 205A Quiz 3, fall semester 2015
Cuesta College, San Luis Obispo, CA

A vector R has a magnitude of 16 m, with a y-component R_y = –5.5 m. 
The x-component R_x is positive. The magnitude of the x-component R_x is:
(A) 3 m.
(B) 5 m.
(C) 15 m.
(D) 17 m.

Correct answer (highlight to unhide): (C)

The magnitude of vector R is the square root of the sum of the squares of its components:

|R| = sqrt(R_x² + R_y²),

such that the R_x can be solved for in terms of the magnitude |R| and y-component R_y:

|R|² = R_x² + R_y²,

|R|² – R_y² = R_x²,

sqrt(|R|² – R_y²) = R_x,

sqrt((16 m)² – (–5.5 m)²) = R_x,

such that (the magnitude of) R_x is 15 m.

Sections 70854, 70855, 73320
Exam code: quiz03re3T
(A) : 3 students
(B) : 1 student
(C) : 68 students
(D) : 2 students

Success level: 80%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.81

Online reading assignment: vector components, projectile motion

Physics 205A, fall semester 2015
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on vector components and projectile motion.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"I learned about the importance of trigonometry in physics and how to use the sin, cos, tan, functions to determine certain angles and figure out how to solve problems with these features. I also learned about vectors and how they deal with both magnitude and direction."

"A projectile has no acceleration in the horizontal axis and that only gravity acts on it, and the path will be a parabola."

"It was interesting when the ball was shot upwards while the cart was moving horizontally and the ball landed to the cart. Projectile motion is just vertical free fall with a constant horizontal component."

"My level of understanding trigonometry is very basic. With a little bit of review on how to apply this to triangles in class I think I could have a better understanding."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"How both the pool balls with different directions hit the ground at the same time."

"Just about all things velocity related."

"Nothing was confusing."

"Probably everything."

Mark the level of your exposure to trigonometry (triangles, unit circles, inverse functions, Pythagorean theorem):

None at all.	[0]
Slight.	*** [3]
Some.	************* [13]
A fair amount.	************************ [24]
A lot.	*********************** [23]

Indicate the following trigonometric relations between angle θ, the opposite leg o, the adjacent leg a, and hypotenuse h for a right triangle. (Assume that the angle θ is in the first quadrant: 0° ≤ θ ≤ 90°.)
(Only correct responses shown.)

sin θ: (o/h) [95%]
cos θ: (a/h) [94%]
tan θ: (o/a) [95%]
hypotenuse h length: √(o² + a²) [97%]

Describe what mnemonic device (if any) you use to memorize the right-triangle trigonometric relationships.

"I don't remember. Oh! Is it SOH-CAH-TOA? One problem--I still don't remember what that stands for."

"SOH-CAH-TOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj. I learned it in ninth grade and it still stuck. There's a story that goes with it that I don't really remember though."

"I don't have one. Only my brain."

Indicate the initial velocity components for the (ideally) vertically-launched anvil.
(Only correct responses shown.)

v_0x: 0 [84%]
v_0y: positive [71%]

Indicate the initial velocity components for the car driven horizontally off the cliff.
(Only correct responses shown.)

v_0x: positive [76%]
v_0y: 0 [51%]

Indicate the initial velocity components for the car launched diagonally off the cliff.
(Only correct responses shown.)

v_0x: positive [81%]
v_0y: positive [62%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"How can I best learn to understand 'physics talk' I'm finding it most difficult to even understand what questions are asking. Should I just be memorizing physics terminology?" (That's a necessary start. But there's much more past that, like concepts and applications.)

"Help! I get the concepts but applying them is not going well." (Okay, but you're nearly there--let's try to get you all the way there before the quiz.)

"I like triangles."

"Do you get to see a lot of things destroyed in physics?" (What is best in life? To crush your students, to see them driven before you, and to hear the lamentations of their parents.)

"What are you plans for Labor Day weekend?" (Hopefully Mrs. P-dog and I will be doing more of this.)

Physics quiz question: direction of vector, given components

Physics 205A Quiz 3, fall semester 2013
Cuesta College, San Luis Obispo, CA

A vector R has x- and y-components as shown at right. The direction of vector R, as measured counterclockwise from the +x direction is:
(A) 115°.
(B) 155°.
(C) 205°.
(D) 245°.

Correct answer (highlight to unhide): (D)

Many calculators do not properly calculate the angle of a vector counterclockwise from the +x axis, instead calculating an angle θ for the related vector in the first quadrant (by dropping ± signs from the R_x and R_y components in the arctangent operation. Thus this "first quadrant angle" θ is:

θ = Arctan|R_y/R_x| = Arctan|(2.4 units)/(1.1 units)| = 65°.

However, since we know that the vector R must be in the third quadrant, then we will need to add this "first quadrant angle" θ to 180° such that the direction of R measured counterclockwise from the +x axis is:

180° + 65° = 245°.

For the cases of vectors in other quadrants, if the vector truly lies in the first quadrant, then its direction is the same as the "first quadrant angle" θ. If the vector lies in the second quadrant, then its direction is the "first quadrant angle" θ subtracted from 180°. If the vector lies in the fourth quadrant, then its direction is the "first quadrant angle" θ subtracted from 360°.

(Response (A) is 180° – 65°; response (B) is 180° – 25°; response (C) is 180° + 25°.)

Sections 70854, 70855, 73320
Exam code: quiz03eL3v
(A) : 13 students
(B) : 3 students
(C) : 10 students
(D) : 44 students

Success level: 63%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.54

Physics quiz question: magnitude of vector, given components

Physics 205A Quiz 3, fall semester 2013
Cuesta College, San Luis Obispo, CA

A vector R has x- and y-components as shown at right. The magnitude of vector R is:
(A) 1.9 m.
(B) 2.6 m.
(C) 7.0 m.
(D) 12 m.

Correct answer (highlight to unhide): (B)

The magnitude of vector R is the square root of the sum of the squares of its components R_x = +1.1 m, R_y = –2.4 m:

| R| = sqrt(R_x² + R_y²) = sqrt((+1.1 m)² + (–2.4 m)²)) = 2.640075756 m,

which to two significant figures is 2.6 m.

Response (A) sqrt(|R_x| + |R_y|); response (C) is (R_x² + R_y²); response (D) is (|R_x| + |R_y|)².

Sections 70854, 70855, 73320
Exam code: quiz03eL3v
(A) : 3 students
(B) : 65 students
(C) : 2 students
(D) : 0 students

Success level: 93%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.13