Physics quiz question: final velocity of falling object

Physics 205A Quiz 2, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 2.45

[3.0 points.] Consider a ball that is thrown vertically upwards with an initial speed of 4.20 m/s from the roof of a building that is 52.7 m tall. Neglect air resistance. With what velocity does the ball strike the ground?
(A) –32.4 m/s.
(B) –32.1 m/s.
(C) –31.9 m/s.
(D) –22.6 m/s.

Correct answer: (A)

Since time is not explicitly given, the most direct approach is to solve for v_f,y using:

(v_fy)^2 - (v_iy)^2 = 2*a_y*delta(y),

where v_iy = +4.20 m/s, a_y = -9.80 m/s^2, and delta(y) = -52.7 m.

Response (B) is using v_iy = 0 (this was the most common error). Response (C) is the result of a sign error in solving for v_fy as sqrt(-v_iy^2 + 2*a_y*delta(y)). Response (D) is the result of v_iy*delta(y)/a_y.

Student responses
Sections 30880, 30881
(A) : 28 students
(B) : 10 students
(C) : 6 students
(D) : 4 students

"Difficulty level": 60%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.87