A 20-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 20-kg object after the collision.
A)-1.0 m/s
B)-2.0 m/s
C)+1.5 m/s
D)+2.0 m/s

Question

Quizplus · Accepted Answer

In an elastic collision, both momentum and kinetic energy are conserved.

Let's denote the initial velocity of the 10-kg object as v. Since it is a head-on collision, its velocity is positive (+3.0 m/s).

Using the conservation of momentum:

(initial momentum) = (final momentum)
10 kg * 3.0 m/s + 20 kg * 0 m/s = 10 kg * v + 20 kg * vf

where vf is the final velocity of the 20-kg object.

Rearranging:

vf = (10 kg * 3.0 m/s + 20 kg * 0 m/s - 10 kg * v) / 20 kg

vf = (30 - 10v) / 20

vf = (3 - v/2) m/s

So the final velocity of the 20-kg object is (3 - v/2) m/s. Since v was positive, it was moving in the positive direction. Therefore, it slowed down the 20-kg object, which was initially at rest. This means that vf is positive, so the answer is +2.0 m/s, choice D.

A 20-Kg Object Sitting at Rest Is Struck Elastically in a Head-On