Physics quiz question: upward-jumping high diver

Physics 205A Quiz 2, fall semester 2012
Cuesta College, San Luis Obispo, CA

An Olympic diver jumps upwards off of a platform and spends 1.78 s in the air until diving into the water 10.0 m below the platform[*]. Neglect air resistance. Choose up to be the +y direction. The diver jumped upwards with an initial speed of:
(A) 3.10 m/s.
(B) 5.62 m/s.
(C) 8.72 m/s.
(D) 14.34 m/s.

[*] youtu.be/9YUtFpLpGfk.

Correct answer (highlight to unhide): (A)

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

(t₀ = 0 s),
(y₀ = 0 m),
t = 1.78 s,
y = –10.0 m,
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 v_0y to be solved for appearing in the third equation, with all other quantities given (or assumed to be known), then:

v_0y·t = y – (1/2)·a_y·(t)²,

v_0y = y/t – (1/2)·a_y·t,

v_0y = (–10.0 m)/(1.78 s) – (1/2)·(–9.80 m/s²)·(1.78 s),

v_0y = –5.62 m/s + 8.72 m/s = +3.10 m/s,

the magnitude of which is speed, or 3.10 m/s.

(Response (B) is y/t; response (C) is (1/2)·a_y·t, response (D) is y/t + (1/2)·a_y·t.)

Sections 70854, 70855
Exam code: quiz02Bo74
(A) : 15 students
(B) : 14 students
(C) : 10 students
(D) : 19 students

Success level: 26%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.24