Physics quiz question: free fall, initial upwards velocity

Physics 205A Quiz 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 2.46(a)

A ball is launched vertically upwards from ground level. It reaches a highest point of 12.0 m above the ground. Neglect air resistance. Choose up to be the +y direction. The ball was launched from ground level with an initial speed of:
(A) 3.83 m/s.
(B) 15.3 m/s.
(C) 16.9 m/s.
(D) 118 m/s.

Correct answer: (B)

At the highest point, ∆y = +12.0 m, and v_fy = 0 m/s. So:

v_fy² - v_iy² = 2·a_y·∆y,

and solving for v_iy:

v_iy = sqrt(-2·a_y·∆y) = sqrt(-2*(-9.80 m/s²)·(+12.0 m)) = ±15.33623161 m/s, or 15.3 m/s, to three significant figures.

Response (A) is -a_y·∆t/2, response (C) is ∆y - a_y/2, response (D) is -a_y·∆y.

Sections 70854, 70855
Exam code: quiz02p4iN
(A) : 0 students
(B) : 47 students
(C) : 3 students
(D) : 2 students

Success level: 89%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.33