Physics quiz question: stalled rocket

Physics 205A Quiz 2, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 2.40

[3.0 points.] Consider a small rocket that is launched from the ground, initially at rest at t = 0 s. After 8.0 s have elapsed, it is 610 m above the ground and is moving upwards (the +y direction) at a speed of 18.0 m/s. Assume that the rocket moves up in a straight line, and neglect air resistance. If the rocket engine shuts off at t = 8.0 s (when it is 610 m above the ground, and is moving upwards at a speed of 18.0 m/s) and undergoes free fall, what velocity does it strike the ground?
(A) –111 m/s.
(B) –109 m/s.
(C) –96 m/s.
(D) –60 m/s.

Correct answer: (A)

Since the time that the rocket will strike the ground is not given, the final velocity v_f,y can be found from the initial velocity v_i,y and the displacement delta(x) (the straight-line vector that points from the initial position to the final position, in this case -610 m):

(v_f,y)^2 - (v_i,y)^2 = 2*a_y*delta(x),

v_f,y = (+/-)sqrt((v_i,y)^2 + 2*a_y*delta(x)),

where the negative root is selected, as the rocket is moving down towards the ground as it strike it.

Response (B) is the velocity of the rocket if it had no initial velocity at 610 m above the ground; responses (C) and (D) solve for the final velocity using v_f,y = v_i,y + a_y*delta(t), assuming that the rocket takes another 8.0 s to strike the ground, with +/- sign error permutations.

Student responses
Sections 70854, 70855
(A) : 22 students
(B) : 13 students
(C) : 8 student
(D) : 4 students

"Difficulty level": 46%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80