A bullet of mass 250g , moving with a horizontal velocity of `400 m*s^(-1)`, gets embedded in a target. The target of mass 4.75 kg can move freely. Find the loss of kinetic energy due to this collision. What happens to this energy loss ?

Explanation

Mass of the bullet , m=250 g=0.25 kg,
velocity of the bullet , `v=400 m*s^(-1)` , and mass of the target, M=4.75 kg.
After the impact , the target and the bullet both move with a velocity V(say).
From the law of conservation of momentum,
mv=(M+m)V
`therefore V=(mv)/(M+m)=(0.25xx400)/(0.25+4.75)=20 m*s^(-1)`.
Kinetic energy of the target and the bullet after collision
`=1/2 (M+m)V^2=1/2 (4.75+0.25)xx20^2=1000J`
Kinetic energy of the target and the bullet after collision
`=1/2mv^2=1/2xx0.25xx(400)^2=20000J.`
Hence, the kinetic energy lost in collision
=20000-1000=19000 J.
This kinetic energy transforms into heat and sound energy.