Physics quiz question: free fall with Despicable Me Minion

Physics 205A Quiz 2, fall semester 2015
Cuesta College, San Luis Obispo, CA

In July 2015 a girl fell out of a third-story apartment window, but landed with only a broken arm, her fall reportedly cushioned with a stuffed Minion doll from the movie Despicable Me.[*] Assume that girl fell 9.0 m downwards, with no initial vertical velocity. Neglect air resistance. Choose up to be the +y direction.

"Toy Department"
Miguel Tejada-Flores
flic.kr/p/re7Xwr

The elapsed time for the girl to fall and reach the ground was:
(A) 1.1 s.
(B) 1.4 s.
(C) 1.8 s.
(D) 2.2 s.

[*] Associated Press, "Police: Minion Toy Broke Girl's Fall from Window," July 20, 2015, wwlp.com/2015/07/20/police-minion-toy-broke-girls-fall-from-window/.

Correct answer (highlight to unhide): (B)

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

(t₀ = 0 s),
(y₀ = 0 m),
y = –9.0 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,

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

1.355261854 s = t,

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

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

Sections 70854, 70855, 73320
Exam code: quiz02J3eP
(A) : 14 students
(B) : 50 students
(C) : 5 students
(D) : 3 students

Success level: 70%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.69