2.5.3 Explosion

Before explosion both object stick together and at rest. After collision, both object move at opposite direction.
Total Momentum before collision Is zero Total Momentum after collision :

m1v1 + m2v2
From the law of conservation of momentum:

Total Momentum Before collision
= Total Momentum after collision

0 = m1v1 + m2v2

m1v1 = - m2v2

(-ve sign means opposite direction)

Example:
A man fires a rifle which has mass of 2.5 kg. If the mass of the bullet is 10 g and it reaches a velocity of 250 m/s after shooting, what is the recoil velocity of the pistol?
Answer:
This is a typical question of explosion.

m1 = 2.5 kg
m2 = 0.01 kg
u1 = 0 ms-1
u2 = 0 ms-1
v1 = ?
v2 = 250 ms-1

By using the equation of conservation of momentum principle
0 = m1v1 + m2v2
0 = (2.5)v1 + (0.01)(250)
(2.5)v1 = -2.5v1 = -1 ms-1