Physics midterm question: thrown upwards vs. downwards balls

Physics 5A Midterm 1, fall semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 3.6

[10 points.] You are standing on a balcony overlooking the beach. You throw and release a ball straight up into the air with an initial speed, and throw and release an identical ball straight down with the same initial speed. Neglect air resistance. Why would they have the same speed when they hit the ground (at different times)? Explain your reasoning using the properties of constant acceleration motion.

Solution and grading rubric:

• p = 10/10: Correct.
  Argues that the ball that was tossed straight up with an initial speed will come back down past its starting point with the same speed, and thus will fall downwards in the same manner from this point onwards as the ball thrown downwards with the same initial speed. Quantitatively this comes from v_fy² - v_iy² = 2·a_y·∆y because of the square of a positive or negative v_iy will result in the same v_fy, but a thorough qualitative argument is sufficient.
  
• r = 8/10:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  
• t = 6/10:
  Nearly correct, but argument has conceptual errors, or is incomplete. Some attempt at incorporating impulse and momentum in discussion. May use a graph, or equations, or argues qualtitatively that the ball that is thrown upwards will start moving downwards from a higher height with zero velocity, and thus will speed up over a greater downward distance to match the final speed of the downwards thrown ball.
  
• v = 4/10:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Argument based on same acceleration, and thus same final velocity, without appealing to how results from v_fy² - v_iy² = 2·a_y·∆y apply, or from the qualitative explanation given in response (p).
  
• x = 2/10:
  Implementation/application of ideas, but credit given for effort rather than merit. Interprets final velocities of balls when they hit the ground as being zero (which would be true after they have hit the ground).
  
• y = 1/10:
  Irrelevant discussion/effectively blank.
  
• z = 0/10:
  Blank.
  

Grading distribution:
p: 19 students
r: 1 student
t: 17 students
v: 6 students
x: 0 students
y: 0 students
z: 0 students

A sample of a "p" response (from student 0036) is shown below: