A 7.6 g bullet is stopped in a block of wood (mw = 3.4 kg). The speed of the bullet-plus-wood combination immediately after the collision is 0.51 m/s.
The sum, of the momenta of bodies mV before collision is equal to the sum after the collision
m1V1 + m2V2 = m1 V1’ + m2 V2’
the conditions of the problem are:
Mass of bullet m1 = 7,6 g = 0,0076 kg
Mass of the block m2 = 3,4 kg
Speed of the block before the collision V2 = 0
The bullet speed equal to the speed of the block after the shock V1 ‘= V2’ = V = 0.51 m / s.
then we have:
m1V1 + m2V2 = (m1 + m2) V
Solving for the velocity of the bullet V1:
V1=[(m1 + m2)V- (m2V2)]/ m1, where m2V2 = 0
V1=(m1 + m2)V/ m1 = (0,0076 + 3,4).(0,51)/0,0076 = 228,6 m/s