Question

A 1.40-kg wooden block rests on a table over a large hole as in the figure below. A 4.60-g bullet with an initial velocity vi is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of 16.0 cm.

(a) Calculate the initial velocity of the bullet from the information provided. (Let up be the positive direction.)

Answer 1

The momentum of the system before and after the collision will be conserved.

So,

mv_i + 0 = (m+M)V

=> (4.6 x 10^-3)v_i = (1.4046)V

now, acceleration = - g = - 9.8 m/s²

final velocity when the system reaches a maximum height of 0.16 m is: v_f = 0 m/s

use,

=>

=> V = 1.771 m/s

this is the velocity of the system just after the collision.

but, (4.6 x 10^-3)v_i = (1.4046)V

so, the initial velocity of the bullet will be:

.