The cue ball $($white$)$ hits the #$3$ ball $($shaded$),$ which is initially at rest.

After the collision, the cue ball's motion is at a $90$ angle to the motion of the object ball, and the #$3$ ball's speed is larger than the cue ball's speed

$,$after

by a factor of V$8$: va$-$bal $=$ V$8$ veter

All balls have the same mass.

$90$

$$What is the ratio of the final and initial speeds of the cue ball $($vatter $/$ ubefore?

$$Show that energy is conserved in this collision