Question

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

Answer 1

According to the work energy theorem 
Loss in Kinetic energy= work done by the frictional force acting on the block

Given: loss of Ek =25%=1/4
thus (1/4)(1/2)mv^2= Fx 
F=(1/8x)mv^2

Let the further distance traveled by the bullet before coming to rest be s+x
Therefore: F(s+x)= 1/2mv^2

Substituting for F we get :
(1/8x)mv^2(s+x)= 1/2mv^2
(s+x)/4x= 1
s+x= 4x
therefore s= 4x-x= 3x