A Particle Is Dropped Vertically On To A Fixed Horizontal Plane. If It Hits The Plane With Velocity ‘u’, Show That It Rebounds With Velocity (-eu).

Ans.

Let \( v \) be the velocity of the particle after collision with the horizontal plane.

\( u \) is the velocity of the particle before collision with the horizontal plane.

If \( e \) be the coefficient of restitution, then

\( \displaystyle{e=\frac{v-0}{u-0}} \)

or, \( \displaystyle{e=\frac{v}{u}} \)

or, \( v=eu \)

Since the direction of the velocity \( v \) is opposite to the direction of \( u \).

So \( v=-eu \).