Question

A bullet of mass 4.5 g is fired horizontally into a 2.4 kg wooden block at rest on a horizontal surface. The bullet is embedded in the block. The speed of the block immediately after the bullet stops relative to it is 2.7 m/s. At what speed is the bullet fired?

Answer 1

First consider the motion of the block-bullet combination for the time interval from the instant just after the bullet embeds itself in the block until the block hits the floor. During this interval, the combination if a projectile with an initial velocity that is horizontal (Vi = 0). The time is found from deltay 2.7 m/s.

Now apply the conservation of momentum:
Vbullet = (1 + (M/m))V = (1 + (2.4*10^3 g/4.6g))(2.7m/s) = 1411.39 m/s

speed is the bullet fired 1411.39 m/s.