Question

As shown in the figure, a small ball is moving with speed $2v$ towards wall $A$ and both the walls are moving with constant velocity $v$ towards each other. Find the speed $v$ in ( 𝑚/𝑠), if the time taken by the ball in first three collision is $5s$. (Assume all collision are perfectly elastic and friction is absent)

Answer 1

$t_1=\frac{1}{3v}$
$t_2=\frac{l-2v\left(t_1\right)}{5v}=\frac{l}{15v}$
$t_3=\frac{l-2v(t_1+t_2)}{7v}=\frac{l}{5\times 7v}$
$t_1+t_2+t_3=\frac{45}{v}=5s$
$v=9m/s$
Final Answer: $9$