1. Two particles, $A$ and $B$, with masses $7m$ and $4m$ respectively are moving towards each other in opposite directions along the same straight line on a smooth horizontal plane when they collide directly. Immediately before the collision, the speed of $A$is $3u$and the speed of $B$ is $5u$. Immediately after the collision, the speed of $A$is ${v}_{A}$ and the speed of $B$ is ${v}_{B}$.

The direction of motion of $A$is reversed after the collision.

Show that ${v}_{B}>\frac{u}{4}$.