Physics midterm problem: skateboard-launched rubber duck toy

Physics 205A Midterm 1, fall semester 2019
Cuesta College, San Luis Obispo, CA

"WRECKING BALL Vs. SEESAW from 45m! How High Will the Watermelon Go?"
How Ridiculous
youtu.be/1quHlRJLtgM

Brett Stanford, Derek Herron and Scott Gaunson for the "How Ridiculous" YouTube channel dropped a heavy ball on one end of a skateboard to launch a rubber duck toy from the other end. Video analysis shows that the toy was launched at an angle of 61° from the horizontal, and took 3.2 s from the moment it was launched from the ground to land back down on the ground. Determine the horizontal distance along the ground from where it was launched to where it landed. Neglect air resistance, and treat the toy as a point object that started on the ground. Show your work and explain your reasoning using properties of projectile motion.

[*] youtu.be/1quHlRJLtgM?t=335.

Solution and grading rubric:

• p:
  Correct. From the time of flight t = 3.2 s, solves for the initial vertical velocity component v_0y = +16 m/s. Next, using the launch angle of elevation θ = 61° finds the initial horizontal velocity component v_0x = +8.7 m/s, and subsequently uses that value and the time of flight t = 3.2 s to solve for the final horizontal position x = +28 m.
• r:
  Nearly correct, but includes minor math errors. At least successfully solves for the vertical v_0y and/or horizontal v_0x components of the initial velocity vector.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least some systematic attempt at using kinematic equations for projectile motion. May have made one or more erroneous assumptions about certain values, such as setting the final velocity components v_x = 0 and or v_y = 0, but still methodically solves for a (wrong) value of v_0y, and then (somehow) solves for a (wrong) value of v_0x using trigonometry to find a (wrong) value for the final horizontal position x.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at systematic use of kinematic equations for projectile motion.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at kinematic equations for projectile motion.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01duCk
p: 15 students
r: 4 students
t: 9 students
v: 21 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 5832):
Another sample "p" response (from student 2342):

Physics quiz question: Casio watch prototype testing

Physics 205A Quiz 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

Casio engineer Kikuo Ibe tested G-Shock watch prototypes by placing them in a rubber ball dropped from a window, falling 10 m down to the ground[*]. Neglect air resistance. Choose up to be the +y direction.

"Story"
Casio America Inc.
gshock.com/technology/story

After being released from rest, the rubber ball took __________ to reach the ground.
(A) 0.49 s.
(B) 1.0 s.
(C) 1.4 s.
(D) 2.0 s.

[*] gshock.com/technology/story.

Correct answer (highlight to unhide): (C)

The following quantities are given (or assumed to be known):

(t₀ = 0 s),
(y₀ = 0 m),
y = –10.0 m (below the starting point),
v_0y = 0 m/s (no initial velocity),
a_y = –9.80 m/s².

So in the equations for constant acceleration motion in the vertical direction, the following quantities are unknown, or are to be explicitly solved for:

v_y = v_0y + a_y·t,

y = (1/2)·(v_y + v_0y)·t,

y = v_0y·t + (1/2)·a_y·(t)²,

v_y² = v_0y² + 2·a_y·y.

With the unknown quantity t to be solved for appearing in the third equation, with all other quantities given (or assumed to be known), then:

y = v_0y·t + (1/2)·a_y·(t)²,

(–10.0 m) = (0 m/s)·t + (1/2)·(–9.80 m/s²)·t²,

1.4285714286 s = t,

or to two significant figures, the elapsed time for the rubber ball to fall is 1.4 s.

(Response (A) is a_y/(2⋅y); response (B) is sqrt(y/a_y); response (D) is 2·y/a_y.)

Sections 70854, 70855
Exam code: quiz02Cs1o
(A) : 2 students
(B) : 17 students
(C) : 29 students
(D) : 6 students

Success level: 54%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.72

Physics quiz archive: kinematics, free fall

Physics 205A Quiz 2, fall semester 2019
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855
Exam code: quiz02Cs1o



Sections 70854, 70855 results

0- 6 :
7-12 :	******** [low = 9]
13-18 :	************
19-24 :	****************** [mean = 21.1 +/- 6.0]
25-30 :	**************** [high = 30]

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.)

Online reading assignment: free fall, vector components

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 presentations on free fall and vector components.


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.

"How to find the right variables for a problem by analyzing which parts of the information are given and which are not. I also understand how to determine which of the kinematic equations to use by determining which of the five variables needs to be found and how to rule out a variable that doesn't need to be found."

"Things can be thrown upwards (start with positive velocity), thrown downwards (start with negative velocity), or dropped (start with zero velocity)."

"During free fall, air resistance is neglected and the acceleration is nearly constant. Because acceleration is constant, we can use kinematic equations. Using a right triangle we are able to define sinθ cosθ and tanθ which helps us solve problems that involve angles. Scalars are numbers with magnitude such as time and volume while vectors are quantities with magnitude and direction such as displacement and velocity."

"I understand that an object can have a different vertical distance traveled than magnitude of vertical displacement. This is dependent on if the object is thrown straight in the air and then free falls, dropped into free fall, or thrown downward. I believe that the vertical displacement is equal to the distance if the object is dropped or thrown down, but the distance traveled is GREATER than the displacement if the object is thrown up."

"The fact that the only force acting on a ball falling down is gravity which has a constant acceleration is consistent with my understanding of physics. I also understand that vectors are determined by the x and y components in a triangle bringing us back to trigonometry.

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 was confused about how an object thrown or shot upwards can reach the same speed when it comes back down to its initial starting point as when it is thrown or shot downwards from its starting point."

"I found the homework problems a little bit confusing just because we haven't gone over many of those sorts of problems together. It would be very helpful to go over one of those specific problems in lecture."

"Trigonometry, but just a refresher would be useful.

Explain what assumptions are made about the amount of drag (air resistance) on an object said to be in free fall.

"We assume that drag forces are negligible."

"Air resistance is ignored."

A boy steps off of a ledge (with no initial vertical velocity) and splashes into the water below.

Choose up to be the +y direction. The initial vertical velocity v_0y has a __________ value.

negative.	*********** [11]
zero.	********************************* [33]
positive.	*** [3]
(Unsure/guessing/lost/help!)	** [2]

For the boy, the vertical distance traveled is __________ the magnitude of the vertical displacement.

less than.	*** [3]
equal to.	************************************ [36]
greater than.	******** [8]
(Unsure/guessing/lost/help!)	** [2]

A ball is thrown and released downwards from the top of a building, and hits the ground below.

Choose up to be the +y direction. The initial vertical velocity v_0y has a __________ value.

negative.	************************* [25]
zero.	********** [10]
positive.	********* [9]
(Unsure/guessing/lost/help!)	***** [5]

For the ball, the vertical distance traveled is __________ the magnitude of the vertical displacement.

less than.	***** [5]
equal to.	**************************** [28]
greater than.	****************** [13]
(Unsure/guessing/lost/help!)	*** [3]

A hat is thrown and released upwards into the air and lands on the grass below.

Choose up to be the +y direction. The initial vertical velocity v_0y has a __________ value.

negative.	**** [4]
zero.	****** [6]
positive.	*********************************** [35]
(Unsure/guessing/lost/help!)	**** [4]

For the hat, the vertical distance traveled is __________ the magnitude of the vertical displacement.

less than.	***** [5]
equal to.	*** [3]
greater than.	************************************** [38]
(Unsure/guessing/lost/help!)	*** [3]

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

None at all.	* [1]
Slight.	*** [3]
Some.	********** [10]
A fair amount.	************************ [24]
A lot.	*********** [11]

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) [92%]
cos θ: (a/h) [88%]
tan θ: (o/a) [88%]
hypotenuse h length: √(o² + a²) [94%]

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

"Soh-cah-toa."

"Don't recall one."

"I've never heard one."

"I don't really use one."

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

"This is pretty cool. We are now moving into free fall which might start to make some things confusing and interesting when combining it with our horizontal motion knowledge."

"For the free fall examples above, would ground level be 0 or from when the ball left their hand?" (The convention used here is that we will always start at y = 0 at t = 0.)

"For all of the questions in this assignment, all of the initial velocities are zero? Because everything starts from not moving and is then thrown?" (If you throw a ball, it won't be in free fall (subject only to the force of gravity) until you let it go--so we can only start time t = 0 from the moment it was released with an initial velocity, as it leaves your hand.)

"Is there ever a setting where the free fall rules for falling objects don't apply?" (If air resistance (drag) is significant, then we can't say that acceleration is a constant value of 9.80 m/s² downwards.)

"In terms of this class are we to automatically assume drag/air resistance doesn't matter or will it be noted?" (On the quizzes and midterms, it will always be stated whether or not air resistance is negligible.)

"The last time I used SOH CAH TOA was 10th grade, so it's a little fuzzy."

"Will we only be using trigonometry to solve problems? I like calculus but I get lost when it comes to applying it to physics for some reason." (We'll use trigonometry to break down diagonal vectors such that we can analyze horizontal and vertical motion separately for projectile motion.)

"Nothing to ask here. Looking forward to the lecture!"

Physics midterm problem: plausible cliff height for ATV jump

Physics 205A Midterm 1, fall semester 2018
Cuesta College, San Luis Obispo, CA

In 2005, Chip Gaines reportedly drove a four-wheeled all-terrain vehicle over an embankment at the edge of a cliff, and became airborne:

I gunned it and launched that four-wheeler straight off the other side of the hill—over a sheer cliff that dropped a good twenty feet to the ground... In a matter of two seconds, the four-wheeler and I...face-planted into the dirt from nearly twenty feet up... And that's how I wound up with this awesome scar.[*]

While Chip Gaines claims that the cliff was 20 ft high (6.0 m), his wife Joanna Gaines recalls that the cliff was only 10 ft high (3.0 m).

Determine which cliff height (6.0 m or 3.0 m) was more plausible for Chip Gaines to be airborne for two seconds after launching himself on his four-wheeler (presumably a 2003 Kawasaki KVF 360 4⨉4[**]) with a speed of 38 mph (17 m/s) at an angle of 30° above the horizontal. Neglect air resistance, and treat Chip Gaines as a point object. Show your work and explain your reasoning using properties of projectile motion.

[*] Chip Gaines, Capital Gaines: Smart Things I Learned Doing Stupid Stuff, W Publishing (2017), pp. 44-47.
[**] kawasakimotorcycle.org/forum/kawasaki-atv-mule/30810-top-speed-360-a.html.

Solution and grading rubric:

• p:
  Correct. From the initial speed of v₀ = 17 m/s and direction of 30° above the horizontal, finds the y-component of initial velocity v_0y = v₀·sinθ = +8.5 m/s; applies projectile motion equations to determine that at t = 2 s, Chris Gaines would be at a final height of y = –2.6 m (thus 2.6 m below his starting point of y₀ = 0), thus making Joanna Gaines' estimate for the cliff height (3.0 m) more plausible that Chris Gaines' estimate of 6.0 m. May instead started with y = –3.0 m and y = –6.0 m and used the quadratic equation to solve for the expected times to reach the bottom of these cliffs, and found that the time to reach a final position of y = –3.0 m is closer to the given t = 2 s.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least some systematic attempt at using kinematic equations for projectile motion.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at systematic use of kinematic equations for projectile motion.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at kinematic equations for projectile motion. Primarily applies trigonometry to find distances rather than velocity components.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01g4iN
p: 31 students
r: 8 students
t: 8 students
v: 3 students
x: 7 students
y: 0 students
z: 1 student

A sample "p" response (from student 0517):

Physics quiz question: vertical golf ball throw

Physics 205A Quiz 2, fall semester 2018
Cuesta College, San Luis Obispo, CA

"1700 GOLF BALLS VS. TRAMPOLINE from 45m!"
How Ridiculous
youtu.be/gz7nk2PylPM

Scott Gaunson for the "How Ridiculous" YouTube channel threw a golf ball up towards the top platform of the Gravity Discovery Centre and Observatory's Leaning Tower of Gingin, near Perth, Australia[*']. Video analysis shows that from the moment it was released from his hand (with an initial upwards speed), the golf ball took 1.8 s to travel 45 m upwards to the top platform, where it still had an upwards speed of 15 m/s. Neglect air resistance. Choose up to be the +y direction. At the moment it left his hand, the golf ball had an initial speed of:
(A) 25 m/s.
(B) 27 m/s.
(C) 33 m/s.
(D) 43 m/s.

[*] youtu.be/gz7nk2PylPM.

Correct answer (highlight to unhide): (C)

The following quantities are given (or assumed to be known):

(t₀ = 0 s),
(y₀ = 0 m),
y = +45 m (level of the top platform above the throw release),
v_y = +15 m/s (moving upwards at the level of top platform),
t = 1.8 s (time when at the level of top platform),
a_y = –9.80 m/s².

So in the equations for constant acceleration motion in the vertical direction, there are no quantities that are unknown, and only one to be explicitly solved for:

v_y = v_0y + a_y·t,

y = (1/2)·(v_y + v_0y)·t,

y = v_0y·t + (1/2)·a_y·(t)²,

v_y² = v_0y² + 2·a_y·y.

Note that as the quantity v_0y to be solved for appears as the only unknown in every one of the equations above, with all other quantities given (or assumed to be known), then any one of these equations could be used to solve for the initial velocity. Here we only demonstrate how the first equation is used:

v_y = v_0y + a_y·t,

+15 m/s = v_0y + (–9.80 m/s²)·(1.8 s),

v_0y = +15 m/s –(–9.80 m/s²)·(1.8 s) = +15 m/s + 17.64 m/s = +32.64 m/s,

or to two significant figures, the initial speed of the golf ball was 33 m/s (in the upwards direction).

(Response (A) is y/t; response (B) is v_f·t; response (D) is v_f·t – (1/2)·a_y·(t²).)

Sections 70854, 70855
Exam code: quiz02HwRd
(A) : 5 students
(B) : 5 students
(C) : 41 students
(D) : 1 student

Success level: 79%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.31

Physics quiz archive: kinematics, free fall

Physics 205A Quiz 2, fall semester 2018
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855 version 1
Exam code: quiz02HwRd



Sections 70854, 70855 results

0- 6 :	** [low = 6]
7-12 :	******
13-18 :	*************
19-24 :	******************** [mean = 20.4 +/- 6.1]
25-30 :	*********** [high = 30]

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.).)

Online reading assignment: free fall, vector components

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 presentations on free fall and vector components.


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 have a a way better understanding of the free fall concept and how gravity affects these objects when thrown in the air and when falling. It was good to have a review of vectors and the trigonometry that goes with calculating them! I feel I have a clearer understanding about what was discussed in class on Monday."

"How to interpret the given equations and use them to solve for an unknown value in a word problem. I also understand that you can manipulate each equation to solve for a different unknown when needed."

"Cosine and sine trigonometric functions allow the x- and y-components of a vector to be calculated."

"How trigonometric functions relate the angles and sides of a right triangle."

"When an object is undergoing free fall, only the force of gravity is pulling on it, so it experiences the acceleration due to gravity, with a magnitude of 9.80 m/s², and since the object is going in a downwards direction, it will always be a negative sign (if up is taken to be the positive vertical direction)."

"That we have to neglect drag on free fall."

"Sorry, I was very busy."

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 not sure when to use the quadratic formula to find time. Also, a little discussion about vertical motion and signs/direction would be helpful."

"The equations. My brain has a harder time making sense of things when there are so many variables with different subscripts. It helps if I can write out a key with what each thing means."

"Some of the equations used were a bit confusing, mostly because I still need to learn the symbols of a lot of things we are learning."

"I would appreciate some review on free falling bodies and the different methods that come with the calculations. I have a better understanding of free falling bodies but i'm still not completely clear on the concept and i'd feel more confident if we discussed in class on Wednesday!"

"I need more explanation on how I assign the signs on the initial velocities for free fall."

"The vectors presentation was pretty confusing for me. I feel that I could use a better explanation."

"I found the vectors section confusing. I understand the steps/equations that are given and when to use them based on the info you have, but the trigonometric functions are unfamiliar to me."

"I don't quite understand the vectors. All the equations and things got to be a little much and I could use a little review in class."

"Nothing really confused me. I understood the basic concepts of everything."

"I'm sorry, P-dog."

Explain what assumptions are made about the amount of drag (air resistance) on an object said to be in free fall.

"When in free fall there is only the force of gravity; there is no air resistance."

"Gravity is the only force affecting an object in free fall."

"When dealing with idealized motion, objects in free fall are not thought to be affected by drag (air resistance)."

"There is no drag on an object said to be in free fall."

"That air resistance is negligible."

"During free fall, it states that in an idealized motion, the air resistance is neglected and the acceleration is nearly constant."

"I have no idea."

A boy steps off of a ledge (with no initial vertical velocity) and splashes into the water below.

Choose up to be the +y direction. The initial vertical velocity v_0y has a __________ value.

negative.	********* [9]
zero.	*********************************** [35]
positive.	*** [3]
(Unsure/guessing/lost/help!)	** [2]

For the boy, the vertical distance traveled is __________ the magnitude of the vertical displacement.

less than.	** [2]
equal to.	***************************************** [41]
greater than.	**** [4]
(Unsure/guessing/lost/help!)	** [2]

A ball is thrown and released downwards from the top of a building, and hits the ground below.

Choose up to be the +y direction. The initial vertical velocity v_0y has a __________ value.

negative.	********************************* [33]
zero.	******** [8]
positive.	****** [6]
(Unsure/guessing/lost/help!)	** [2]

For the ball, the vertical distance traveled is __________ the magnitude of the vertical displacement.

less than.	***** [5]
equal to.	********************************* [33]
greater than.	******** [8]
(Unsure/guessing/lost/help!)	*** [3]

A hat is thrown and released upwards into the air and lands on the grass below.

Choose up to be the +y direction. The initial vertical velocity v_0y has a __________ value.

negative.	*** [3]
zero.	******* [7]
positive.	************************************ [36]
(Unsure/guessing/lost/help!)	*** [3]

For the hat, the vertical distance traveled is __________ the magnitude of the vertical displacement.

less than.	** [2]
equal to.	****** [6]
greater than.	************************************ [36]
(Unsure/guessing/lost/help!)	***** [5]

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

None at all.	* [1]
Slight.	**** [4]
Some.	***** [15]
A fair amount.	**************** [16]
A lot.	************* [13]

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) [88%]
cos θ: (a/h) [90%]
tan θ: (o/a) [88%]
hypotenuse h length: √(o² + a²) [86%]

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

"Soh-cah-toa."

The CAST rule is the way I memorize (positive) trigonometric functions."

"I do not remember them. "I do not have a mnemonic device to memorize any right-triangle trigonometric relationships."

"I just memorized the relations and studied each one because I had to know them."

"I do not use one currently but I would like to learn one."

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

"when you throw a ball downwards the graph is considered to have a negative initial velocity correct? However would the vertical distance traveled be considered to be equal to the magnitude of vertical displacement? Since we don't have a positive initial velocity and the object is dropping from its initial to its final position without rising at any point, then that drop is considered a 'straight line' if you will, hence the vertical distance traveled should be equal to magnitude of vertical displacement right? (Yes, yes, yes.)

"If you could go over the answers for the questions regarding the vertical distance traveled that would be great."

"We need to go over distance vs displacement again, specifically when it is implied with these problems about free-fall." (We certainly will.)

"I know where we can see our quiz grades, but how do we keep track of the points we earn from quiz extra-credit, post-labs, reading assignments, and homework reports?" (All those points are also posted on the same page as the quiz scores. (Lab points will be posted separately, later.))

"Will we only be using the first quadrant?"

"Could you go into vector components a little more? The book makes it kind of confusing."

"Please help on the trigonometry part of this lesson!"

"How far in depth are we going to get into trigonometry? (For now, not that far. We'll use more trigonometry, and review more of it later on, as needed.)

"Is drag the equivalent of friction but in a vertical sense?" (Yes, in the sense that it is a force that always acts against the motion of an object.)

"I am getting better at this style of teaching but it is still taking time to get used to. Personally I think I just do better when material is covered more in class than at home." (I will try to cover as much stuff in class that you tell me that you need to know.)