Question

Three objects $A, B$ and $C$ are kept in a straight line on a frictionless surface. These have masses $m, 2 \,m$ and $2 \,m$, respectively. The object $A$ moves towards $B$ with a speed $9\, m / s$ and makes an elastic collision with it. Thereafter,$ B$ makes an elastic collision with $C$. All motions occur on the same straight line. The final speed (in $m / s$ ) of object $B$ is found to be $x$. Find the value of ' $x$ '.

Answer 1

Collision between $A$ and $B$,
$m \times 9=m_{1}+2 m v_{2}$
$9=v_{1}+2 v_{2}\,\,\,...(1)$
$e=1=\frac{\left(v_{2}-v_{1}\right)}{9}$
$v_{2}-v_{1}=9\,\,\,...(2)$
from (1) and (2)
$v_{2}=6 \,m / s$

$2 m \times 6=3 m \times v _{3}$
$v _{3}=4 \,m / s$