A gun of mass 5 tons fires a bullet of mass 20g with a velocity of 110

1.	A gun of mass 5 tons fires a bullet of mass 20g with a velocity of 110.2 ms-1. Find the velocity of the gun.
Answer» Initially, both the gun and the bullet are at rest. ∴ The total initial momentum of the system is f zero. If v₁ and v₂ are the final velocity of the gun and the bullet, final momentum is given by, p_f = m₁v₁+ m₂v₂ According to the law of conservation of momentum, p_i = p_f m₁v₁ + m₂v₂ = 0 i.e., v₁= – m₂v₂/m₁ _{= \(\frac {-20 \times 110.2}{5 \times 1000}\)} = – 0.44 ms^-1 ∴ Recoil velocity of the gun is 0.44 ms^-1 .

A gun of mass 5 tons fires a bullet of mass 20g with a velocity of 110.2 ms-1. Find the velocity of the gun.

Answer»

Initially, both the gun and the bullet are at rest.

∴ The total initial momentum of the system is f zero.

If v₁ and v₂ are the final velocity of the gun and the bullet, final momentum is given by,

p_f = m₁v₁+ m₂v₂

According to the law of conservation of momentum, p_i = p_f

m₁v₁ + m₂v₂ = 0

i.e., v₁= – m₂v₂/m₁

_{= \(\frac {-20 \times 110.2}{5 \times 1000}\)}

= – 0.44 ms^-1

∴ Recoil velocity of the gun is 0.44 ms^-1 .