From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of ` 35 ms^(-1)` Calculate the recoil velocity of the rifle.

Explanation

Mass of the bullet, `m_(1)`
`= 50 g = (50)/(1000)kg = 0.05 kg`
Mass of the rifle, `m_(2) = 4kg`
Initial velocity of the bullet , `u_(1) = 0 ms^(-1)`
Initial velocity of the bullet, `u_(2) = 0 ms^(-1)`
Final velocity of bullet, `v_(1) = 35 ms^(-1)`
Final velocity of rifle `v_(2)`
According to law of conservation of momentum,
Total momentum before the fire = Total momentum after the fire
`m_(1)u_(1) + m_(2)u_(2) = m_(1)v_(1) + m_(2)v_(2)`
`rArr 0.05 kg xx 0 ms^(-1) + 4 kg xx 0 ms^(-1) = 0.05 kg xx 35 ms^(-1) + 4kg xx v_(2)`
`rArr 0 = 1.75 kg ms^(-1) + 4 kg v_(2)`
`rArr v_(2) = (1-.75 kg ms^(-1))/(4 kg)`
`=0.4375 ms^(-1)`