Physics quiz question: horizontally-thrown projectile

Physics 205A Quiz 3, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 3.46

A ball is thrown off the edge of a cliff with an initial horizontal velocity. It lands on the ground below 1.9 s after it was thrown, at a horizontal distance of 32 m from the base of the cliff. Neglect air resistance. Choose up to be the +y direction. The initial (horizontal) speed of the ball is:
(A) 5.2 m/s.
(B) 17 m/s.
(C) 19 m/s.
(D) 61 m/s.

Correct answer (highlight to unhide): (B)

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

(x₀ = 0 m),
(y₀ = 0 m),
(t₀ = 0 s),
t = 1.9 s,
x = +32 m,
v_0y = 0 m/s,
a_y = –9.80 m/s².

So in the equations for projectile motion, the following quantities are unknown, or are to be explicitly solved for:

x = v_0x·t,

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_0x to be solved for appearing in the fourth equation, with all other quantities given (or assumed to be known), then the initial horizontal velocity can be solved for:

v_0x = x/t = +16.84 m/s,

of which the magnitude (speed) is 17 m/s to two significant digits.

(Response (A) is the result of (9.80 m/s²)/t; response (C) is (9.80 m/s²)·t, which would be the magnitude of the vertical (downwards) velocity of the ball 1.9 s after it was thrown; while response (D) is x·t.)

Student responses
Sections 30880, 30881
(A) : 1 student
(B) : 36 students
(C) : 11 students
(D) : 0 students

Success level: 75%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.43