Question

In the given figure all collisions are head on elastic. Then velocity of ball $c$ after collision is $\frac{8v_o}{3n}$, here $n$ is (Answer upto two decimal places )

Answer 1

After collision of ball A with ball B:
The collision being head on elastic, we can say
$e=1=\frac{v_A-(-v_B)}{v_0}\Rightarrow v_0=v_A+v_B.......\left(1\right)$
and using conservation of momentum,
$m{v}_0=2m{v}_B+m(-v_A).......\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$, $v_B=\frac{2v_0}{3}......\left(3\right)$
Now ball B, with this velocity collides with ball C.
Again,
$1=\frac{v_C-(-v_B^{\prime })}{v_B}\Rightarrow v_B=v_C+v_B^{\prime }.......\left(4\right)$
and
$2m{v}_B=2m(-v_B^{\prime })+3m{v}_C.......\left(5\right)$

After solving equations $\left(3\right)$, $\left(4\right)$ and $\left(5\right)$
We get $v_C=\frac{8}{15}{v}_0\Rightarrow n=5$