A bullet is fired on a fixed target. It penetrates inside the target through distance `d = 3.75 cm` and then stops. mass of the bullet is `m = 1 kg` and of the target is `M = 4 kg`. Now an identical bullet moving with the same velocity is fired on the identical target which is placed at rest on a frictionless horizontal surface. Then find the distance (in cm) to which the bullet will penetrate inside the target?

Answer

3

Explanation

For first case: `W=/_\KEimplies-Rd=-1/2"mu"^(2)`
`Rd=1/2"mu"^(2)`……i
For second case `"mu"=(M+m)v, v` is common velocity
`implies v=m/((M+m))u`
`-Rd'=1/2(M+m)v^(2)-1/2"mu"^(2)=1/2(m^(2)u^(2))/((M+m))-1/2"mu"^(2)`
`implies Rd'=1/2(Mm)/((M+m))u^(2)`
Solving eqn i and ii `(Rd)/(Rd')=(M+m)/Mimpliesd'=3 cm`