Physics quiz question: bounced bullet

Physics 5A Quiz 4, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 7.42

[3.0 points.] A 0.030 kg bullet traveling at 220 m/s in the +x direction hits a motionless 1.4 kg block and bounces off it, retracing its original path with a velocity of 170 m/s in the –x direction. What is the final speed of the block? Assume the block rests on a perfectly frictionless surface.
(A) 1.1 m/s.
(B) 3.6 m/s.
(C) 4.7 m/s.
(D) 8.4 m/s.

Correct answer: (D)

Since there are no external horizontal impulses, momentum is conserved. The total initial momentum is due only to the bullet, p_1,i = m_1*v_1,i = 6.6 kg*m/s. The total final momentum is due to the bullet and the block, where p_1,f + p_2,f = m_1*v_1,f + m_2*v_2,f = -5.1 kg*m/s + m_2*v_2,f; such that equating p_1,i = p_1,f + p_2,f gives:

v_2,f = (m_1*v_1,i – m_1*v_1,f)/m_2,

which is response (D). Response (A) is (m_1*v_1,i + m_1*v_1,f)/m_2; response (B) is m_1*v_1,f/m_2; while response (C) is m_1*v_1,i/m_2.

Student responses
Sections 4987, 4988
(A) : 10 students
(B) : 2 students
(C) : 12 students
(D) : 12 students