A 25.0-kg object sitting at rest is struck elastically in a head-on collision with a 20.5-kg object initially moving at +4.0 m/s.Find the final velocity of the 25.0-kg object after the collision.
A)−0.90 m/s
B)−3.6 m/s
C)+6.6 m/s
D)+3.6 m/s
E)+15 m/s

Question

Quizplus · Accepted Answer

Using conservation of momentum:
m1v1i + m2v2i = m1v1f + m2v2f
(25 kg)(0 m/s) + (20.5 kg)(4.0 m/s) = (25 kg)(v1f) + (20.5 kg)(v2f)
Solving for v1f:
v1f = (m2/m1)(v1i - v2i) + v2f
v1f = (20.5 kg/25.0 kg)(0 m/s - 4.0 m/s) + 4.0 m/s
v1f = -3.6 m/s
The negative sign indicates that the final velocity of the 25.0-kg object is in the opposite direction of the initial velocity of the 20.5-kg object. Therefore, the correct choice is D) +3.6 m/s.

A 250-Kg Object Sitting at Rest Is Struck Elastically in a a Head-On