Physics quiz question: impulse on rebounding projectile

Physics 205A Quiz 4, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 7.7, 7.49

A 0.55 kg projectile heads towards a wall with a speed of 12.0 m/s, and after colliding, rebounds in the reverse direction along the same line with a speed of 5.0 m/s. Neglect friction and drag. The magnitude of the impulse exerted on the projectile is:
(A) 2.8 N·s.
(B) 3.9 N·s.
(C) 6.6 N·s.
(D) 9.4 N·s.

Correct answer (highlight to unhide): (D)

The impulse exerted on the projectile is given by:

J = ∆p,

J = m·(v_f – v₀) = (0.55 kg)·((–5.0 m/s) – (+12 m/s)) = –9.35 kg·m/s,

or to two significant figures, the magnitude of the impulse exerted on the projectile is 9.4 N·s.

Note that since the initial velocity v₀ = +12 m/s is taken to be in the positive direction, then the final velocity that rebounds in the "reverse direction" must be negative: v_f = –5.0 m/s.

(Response (A) is the magnitude of the final momentum; response (B) is the difference in the magnitudes of the final and initial momenta; while response (C) is the magnitude of the initial momentum.)

Student responses
Sections 30880, 30881
(A) : 3 students
(B) : 13 students
(C) : 14 students
(D) : 12 students

Success level: 27%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.60