# Question #b6c63

Dec 17, 2016

There appears to be some missing text in the opening sentence of the question.

Assuming it is as follows:

"A golf ball collides elastically with a bowling ball initially at rest and bounces back."

It is given that the golf ball bounces back with tiny loss in its incident speed.

Let ${m}_{g}$ be mass of golf ball and ${v}_{i}$ be its initial velocity. Let ${M}_{b}$ be the mass of bowling ball. And ${p}_{b}$ be final momentum of bowling ball.
Initial momentum of the system is
${p}_{i} = {m}_{g} \times {v}_{i} + {M}_{b} \times 0$
$\implies {p}_{i} = {m}_{g} {v}_{i}$ .......(1)

Final momentum ${p}_{f}$ is
${p}_{f} = {m}_{g} \times \left(- {v}_{i}\right) + {p}_{b}$
$\implies {p}_{f} = - {m}_{g} {v}_{i} + {p}_{b}$ .....(2)

Using law of conservation of momentum, we equate (1) with (2). We get
${m}_{g} {v}_{i} = - {m}_{g} {v}_{i} + {p}_{b}$
$\implies {p}_{b} = 2 \left({m}_{g} {v}_{i}\right)$ ....(3)

We see that after collision, bowling ball recoils with twice the initial momentum of golf ball.