Physics quiz question: Penguin B UAV catapult time

Physics 205A Quiz 2, fall semester 2013
Cuesta College, San Luis Obispo, CA

"6 kJ Portable Pneumatic Catapult"
UAV Factory
uavfactory.com/product/21

A portable pneumatic catapult[*] is able to launch a Penguin B unmanned aerial vehicle (UAV) from rest to a final speed of 23 m/s along a 4.0 m rail. Assume that the rail is horizontal, and that acceleration of the UAV starting from rest to when it is launched is constant, and always points in the same direction as its velocity. The elapsed time for the UAV be catapulted from rest to its final speed is:
(A) 0.35 s.
(B) 0.60 s.
(C) 0.90 s.
(D) 2.9 s.

[*] UAV Factory, "6 kJ Portable Pneumatic Catapult," uavfactory.com/product/21.

Correct answer (highlight to unhide): (A)

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

(x₀ = 0 m),
x = +4.0 m,
v_0x = 0 m/s,
v_x = +23 m/s.

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

v_x = v_0x + a_x·t,

x = (1/2)·(v_x + v_0x)·t,

x = v_0x·t + (1/2)·a_x·(t)²,

v_x² = v_0x² + 2·a_x·x.

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

x = (1/2)·(v_x + v_0x)·t,

t = 2·x/(v_x − v_0x) = 2·(+4.0 m)/(+23 m/s + 0 m/s) = 0.347826087 s,

or to two significant figures, t = 0.35 s.

(Response (B) is sqrt(v_x)/(2·x); response (C) is t = sqrt(2·x/(9.80 m/s²)); response (D) is v_x/(2·x).)

Sections 70854, 70855, 73320
Exam code: quiz02p3nG
(A) : 55 students
(B) : 7 students
(C) : 2 students
(D) : 4 students

Success level: 80%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.54