A 30-kg object sitting at rest is struck elastically in a head-on collision with a 10-kg object initially moving at +3.0 m/s.Find the final velocity of the 30 kg object after the collision.
A) −1.0 m/s
B) +1.2 m/s
C) +1.5 m/s
D) +2.0 m/s

Question

Quizplus · Accepted Answer

Since it is an elastic collision, we can use the following equation:
m1v1 + m2v2 = m1v1' + m2v2'
where
m1 = 30 kg
v1 = 0 (initial velocity of the 30-kg object)
m2 = 10 kg
v2 = 3.0 m/s (initial velocity of the 10-kg object)
v1' = final velocity of the 30-kg object
v2' = final velocity of the 10-kg object (but we don't need to find this)

Substituting the values in the equation, we get
(30 kg) (0 m/s) + (10 kg) (3.0 m/s) = (30 kg) (v1') + (10 kg) (v2')
Simplifying and solving for v1', we get
v1' = (10 kg)(3.0 m/s) / (30 kg) = 1.0 m/s
But since the 10-kg object was moving in the positive direction, the final velocity of the 30-kg object would also be positive, so the answer is
Choice C, +1.5 m/s.

A 30-Kg Object Sitting at Rest Is Struck Elastically in a Head-On