Question

Two rubber balls have an elastic head-on collision with each other. One ball has a mass of 0.25 kg and an initial velocity of 5.00 m/s. The other has a mass of 0.80 kg and is initially at rest. No external forces act on the ball. What are the velocities of the balls after the collision?

Answer 1

Apply momentum conservation^ initial momentum equals to the final momentum (after the collision):

$$p_i=p_f.$$

The initial is

$$p_i=0.25\cdot5=1.25\text{ N s}.$$

The final consists of momenta of both balls:

$$p_f=0.25v+0.8u.$$

So, we have

$$1.25=0.25v+0.8u.$$

To find the velocities, apply kinetic energy conservation as well:

$$\frac12 0.25\cdot5^2=\frac12 0.25v^2+\frac12 0.8u^2.$$

So, we have two equations, and the solution is

$$v=-2.62\text{ m/s (the 0.25kg ball rebounds)},\\ u=2.38\text{ m/s}.$$