20181012

Physics midterm question: position of vertically-launched ball

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

A Physics 205A student slings a ball straight upwards. The vy(t) graph of this ball is shown at right, starting from when the ball was released at y = 0 at t = 0. Neglect air resistance. Choose up to be the +y direction. At t = 6 s, discuss why the ball is at a position higher than its release point. Explain your reasoning using the properties of velocity, position, distance traveled, and/or displacement.

Solution and grading rubric:
  • p:
    Correct. Supports claim that the ball is still above its release point at t = 6 s by discussing at least one of the following explanations:
    1. displacement is the bounded area between the velocity function and the time axis, and since there is a greater bounded area above the time axis (corresponding to a positive displacement for t = 0 to 4 s) than the bounded area below the time axis (corresponding to a negative displacement for t = 4 s to 6 s), the ball has traveled farther up from its starting point to its highest height, than traveling downwards from its highest height to its final position at t = 6 s; or
    2. the ball slows down from an upwards velocity of +40 m/s at t = 0 to zero velocity at its highest point at t = 4 s, and from symmetry, the ball should fall back down to its starting point with a downwards speed of –40 m/s at t = 8 s, such that the ball is still somewhere above its starting point at t = 6 s; or
    3. uses kinematic equations for constant motion to show that the final position at t = 6 s is still positive.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear 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: midterm01g4iN
p: 24 students
r: 5 students
t: 21 students
v: 8 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1414):

Another sample "p" response (from student 3691):

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