Question

A bullet is fired normally on an immovable wooden plank. it loses 25% of its momentum in penetrating a thickness 3.5cm of the plank. what is the total thickness penetrated by the bullet.

Answer 1

75% of the momentum is wasted in travelling the path and rest 25% wasted in penetrating the wooden block so let's suppose that

The mass of the bullet is m

And the initial velocity is u

The 25% of its kinetic energy is

1/8×mv^2

And work done in penetrating the block is

F×x

So from the law of conservation of energy

F×x=1/8mv^2

Since f=ma

And here retardation has been occurred, as ball is stopped, so

a=(v-u)/t

Here v=0

Hence

1/8mu^2=mux

X=1/8×u

Hence the ball will penetrate the block equals to one eighth of its initial velocity if it uses 25% of its kinetic energy in doing so