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):