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: 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

Physics quiz question: soccer ball vertical velocity component

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

A Physics 205A student kicks a soccer ball off a cliff with an initial velocity vector that has x- and y-components:

v_0x = +6.1 m/s,
v_0y = –3.2 m/s.

Neglect air resistance. Just before it hits the ground, the magnitude of the soccer ball's vertical velocity is:
(A) 0 m/s.
(B) some value between 0 m/s and 3.2 m/s.
(C) 3.2 m/s.
(D) some value greater than 3.2 m/s.

Correct answer (highlight to unhide): (D)

While the horizontal component of the soccer ball's velocity never changes, the vertical component of the soccer ball's velocity will always keep changing, due to the acceleration due to gravity. The soccer ball already starts with an initial downwards speed, and the vertical downwards speed will increase as it keeps moving along its trajectory.

Sections 70854, 70855
Exam code: quiz03Ch3V
(A) : 6 students
(B) : 5 students
(C) : 19 students
(D) : 24 students

Success level: 44%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.86

Physics quiz archive: vectors, projectile motion, forces

Physics 205A Quiz 3, fall semester 2019
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855
Exam code: quiz03Ch3V



Sections 70854, 70855 results

0- 6 :	* [low = 6]
7-12 :	***
13-18 :	**************
19-24 :	******************* [mean = 21.7 +/- 5.8]
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.)

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: 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

Physics quiz question: basketball horizontal velocity component

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

A Physics 205A student throws a basketball with an initial velocity vector that has x- and y-components:

v_0x = +5.5 m/s,
v_0y = +4.2 m/s.

Neglect air resistance. At the highest point in its trajectory, the magnitude of the basketball's horizontal velocity is:
(A) 0 m/s.
(B) some value between 0 m/s and 5.5 m/s.
(C) 5.5 m/s.
(D) some value greater than 5.5 m/s.

Correct answer (highlight to unhide): (C)

For the ideal case of projectile motion where air resistance is negligible, the vertical component of the ball's velocity continuously changes (due to the downwards vertical acceleration due to gravity), while the horizontal component of the ball's velocity remains constant (due to there being no horizontal acceleration).

Sections 70854, 70855
Exam code: quiz03pRH5
(A) : 3 students
(B) : 8 students
(C) : 38 students
(D) : 6 students

Success level: 68%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.73

Physics quiz question: basketball vertical velocity component

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

A Physics 205A student throws a basketball with an initial velocity vector that has x- and y-components:

v_0x = +5.5 m/s,
v_0y = +4.2 m/s.

Neglect air resistance. At the highest point in its trajectory, the magnitude of the basketball's vertical velocity is:
(A) 0 m/s.
(B) some value between 0 m/s and 4.2 m/s.
(C) 4.2 m/s.
(D) some value greater than 4.2 m/s.

Correct answer (highlight to unhide): (A)

The horizontal component of the ball's velocity never changes, while the vertical component of the ball's velocity is changing: as it moves upwards before reaching its highest point, the ball's vertical velocity component points upwards; while at the moment it is at the highest point in its trajectory, the vertical component of the ball's velocity is zero; and as it moves downwards after reaching the highest point, the vertical component of the ball's velocity points downwards.

Sections 70854, 70855
Exam code: quiz03pRH5
(A) : 37 students
(B) : 4 students
(C) : 9 students
(D) : 6 students

Success level: 66%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.67

Physics quiz question: distance traveled vs. displacement magnitude

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

A Physics 205A student throws a basketball with an initial velocity vector that has x- and y-components:

v_0x = +5.5 m/s,
v_0y = +4.2 m/s.

Neglect air resistance. From being launched to reaching the highest height of its trajectory, the basketball's distance traveled will be __________ the magnitude of its displacement.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

For projectile motion, the distance traveled is measured along its curved trajectory, and is longer than the magnitude of the displacement, which is the length of the straight-line vector that starts from the release point, and ends at the highest point of its trajectory.

(Response (A) can never be true for any possible path taken by an object. Response (B) can only be true for an object traveling along a straight-line with no reversals in direction.)

Sections 70854, 70855
Exam code: quiz03pRH5
(A) : 4 students
(B) : 12 students
(C) : 40 students
(D) : 0 students

Success level: 71%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.53

Physics quiz archive: vectors, projectile motion, forces

Physics 205A Quiz 3, fall semester 2018
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855 version 1
Exam code: quiz03pRH5



Sections 70854, 70855 results

0- 6 :
7-12 :	***** [low = 9]
13-18 :	**********
19-24 :	******************* [mean = 23.1+/- 6.0]
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.).)

Physics midterm problem: world-record washing machine throw

Physics 205A Midterm 1, fall semester 2017
Cuesta College, San Luis Obispo, CA

"Washing Machine Throwing Showdown"
Guinness World Records
youtu.be/YC0oj7BcWiI

In 2017, Zydrunas Savickas set a world record throwing a 46 kg (101 lb) washing machine that landed a horizontal distance of 4.13 m from its starting position atop his head. Savickas' height is 1.91 m, and the washing machine was airborne for 1.84 s starting from just off the top of his head to just before hitting the ground[*].

Find both the horizontal and vertical components (v_0x, v_0y) of the initial velocity vector for the washing machine, as it was thrown and released from just above the top of Savickas' head. Neglect air resistance, and treat the washing machine as a point object. Show your work and explain your reasoning using properties of projectile motion.

[*] Rachel Swatman, "Watch Game of Thrones Star Take on World’s Strongest Man Winner in Washing Machine Throwing Showdown" (January 13, 2017), guinnessworldrecords.com/news/2017/1/watch-game-of-thrones-star-take-on-world%E2%80%99s-strongest-man-winner-in-washing-machi-458290.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates:
  1. uses given values of t = 1.84 s and x = +4.13 m to solve for the initial (and constant) horizontal velocity v_0x (where t₀ = 0, x₀ = 0); and
  2. uses given values of t = 1.84 s and y = −1.91 m to solve for the initial vertical velocity v_0y (where t₀ = 0, y₀ = 0).
• r:
  Nearly correct, but includes minor math errors. May have intentionally or unintentionally used y = +1.91 m or y = 0 instead of y = −1.91 m.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has one initial velocity component correct, but other component has errors in addition to those listed in (r), such as setting v_y = 0 in y = (1/2)⋅(v_y0 + v_y)⋅t to solve for v_y0, or setting v_x = 0 in x = (1/2)⋅(v_0x + v_x)⋅t to solve for v_x0, etc.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
• x:
  Implementation of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01mOoL
p: 20 students
r: 16 students
t: 12 students
v: 3 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1956):

Physics quiz question: Skycycle X-2 average speed vs. magnitude of average velocity

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

"Evel Knievel's Skycycle"
Tennessee Dept. of Tourism
tnsjournal.com/entertainment/history-channel-museum-men-filming-sevierville/

Evel Knievel's Skycycle X-2 rocket ship was launched with an initial speed of 44 m/s at an angle of 56° above the horizontal[*]. Neglect air resistance, and treat the rocket as a thrown object. From being launched to reaching the highest height of its trajectory, the rocket ship's average speed will be __________ the magnitude of its average velocity.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

[*] James Vlahos, "The Devils And The Deep Blue Sky," popsci.com/article/technology/devils-and-deep-blue-sky, (September 24, 2014).

Correct answer (highlight to unhide): (C)

The average speed of the rocket ship is its distance traveled divided by elapsed time, while the magnitude of average velocity is given by the magnitude of displacement divided by elapsed time. For projectile motion, the distance traveled is measured along its curved trajectory, and is longer than the magnitude of the displacement, which is the length of the straight-line vector that starts from the ground, and ends at the highest point of its trajectory. Since the elapsed time for the rocket ship to travel from the start to finish is the same whether along the actual distance traveled or the straight-line displacement, the average speed of the rocket ship must be greater than the magnitude of its average velocity.

(Response (A) can never be true for any possible path taken by an object. Response (B) can only be true for an object traveling along a straight-line with no reversals in direction.)

Sections 70854, 70855
Exam code: quiz03T4uC
(A) : 6 students
(B) : 10 students
(C) : 32 students
(D) : 0 students

Success level: 59%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.63

Physics quiz archive: vectors, projectile motion, forces

Physics 205A Quiz 3, fall semester 2017
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855 version 1
Exam code: quiz03T4uC



Sections 70854, 70855 results

0- 6 :
7-12 :	********* [low = 9]
13-18 :	****************
19-24 :	*********************** [mean = 19.2 +/- 5.2]
25-30 :	****** [high = 27]

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)