A bullet is fired normally on an immovable plank of wood. It loses 25% of its kinetic energy in penetrating a thicknees x of the plank. What is the total thickness penetrated by the bullet?

Let ‘u’ be the initial velocity of the bullet of mass ‘m’.

Initial kinetic energy = ½ mu²

If ‘v’ is the final velocity then,

Final kinetic energy = ½ mv² = ½ mu² – ½ mu² × 25/100

=> v² = 0.75u²

Suppose, the acceleration of the bullet is ‘a’.

Then, v² = u² + 2ax

=> a = (v² – u²)/(2x)

=> a = (0.75u² – u²)/2x

=> a = -0.25u²/(2x)

With this acceleration the bullet penetrates until it comes to rest. If, ‘s’ is the total penetration then,

Using,

v² = u² + 2as

=> 0 = u² + 2{-0.25u²/(2x)}s

=> s = x/0.25 = 4x

So, the total penetration of the bullet is 4x.