Physics quiz question: Casio watch prototype testing

Physics 205A Quiz 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

Casio engineer Kikuo Ibe tested G-Shock watch prototypes by placing them in a rubber ball dropped from a window, falling 10 m down to the ground[*]. Neglect air resistance. Choose up to be the +y direction.

"Story"
Casio America Inc.
gshock.com/technology/story

After being released from rest, the rubber ball took __________ to reach the ground.
(A) 0.49 s.
(B) 1.0 s.
(C) 1.4 s.
(D) 2.0 s.

[*] gshock.com/technology/story.

Correct answer (highlight to unhide): (C)

The following quantities are given (or assumed to be known):

(t₀ = 0 s),
(y₀ = 0 m),
y = –10.0 m (below the starting point),
v_0y = 0 m/s (no initial velocity),
a_y = –9.80 m/s².

So in the equations for constant acceleration motion in the vertical direction, the following quantities are unknown, or are to be explicitly solved for:

v_y = v_0y + a_y·t,

y = (1/2)·(v_y + v_0y)·t,

y = v_0y·t + (1/2)·a_y·(t)²,

v_y² = v_0y² + 2·a_y·y.

With the unknown quantity t to be solved for appearing in the third equation, with all other quantities given (or assumed to be known), then:

y = v_0y·t + (1/2)·a_y·(t)²,

(–10.0 m) = (0 m/s)·t + (1/2)·(–9.80 m/s²)·t²,

1.4285714286 s = t,

or to two significant figures, the elapsed time for the rubber ball to fall is 1.4 s.

(Response (A) is a_y/(2⋅y); response (B) is sqrt(y/a_y); response (D) is 2·y/a_y.)

Sections 70854, 70855
Exam code: quiz02Cs1o
(A) : 2 students
(B) : 17 students
(C) : 29 students
(D) : 6 students

Success level: 54%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.72