Problem

Figure 2

Figure 2 shows two particles, $A$ and $B$, moving in opposite directions on a smooth horizontal surface. Particle $A$ has mass $5\text{ kg}$ and particle $B$ has mass $x\text{ kg}$.

The particles collide directly.

Immediately before the collision, the speed of $A$ is $3\text{ m s}^{-1}$ and the speed of $B$ is $x\text{ m s}^{-1}$

Immediately after the collision, the speed of $A$ is $1\text{ m s}^{-1}$ and its direction of motion is unchanged.

Immediately after the collision, the speed of $B$ is $1.5\text{ m s}^{-1}$

(a) Find the value of $x$.

(b) Find the magnitude of the impulse exerted on $A$ by $B$ in the collision.