Problem

7.

Particle $A$ of mass $3m$ is moving in a straight line with speed $2u$ on a smooth horizontal surface. Particle $A$ collides directly with particle $B$ of mass $m$, which is moving along the same straight line and in the same direction as $A$.

Immediately before the collision, the speed of $B$ is $u$.

As a result of the collision, the direction of motion of $B$ is unchanged and the kinetic energy gained by $B$ is $\frac{48}{25}mu^2$

(a) Find the coefficient of restitution between $A$ and $B$.

After the collision, $B$ hits a smooth fixed vertical wall that is perpendicular to the direction of motion of $B$. The coefficient of restitution between $B$ and the wall is $f$.

Given that the speed of $B$ immediately after first hitting the wall is equal to the speed of $A$ immediately after its first collision with $B$,

(b) find the value of $f$.