Question

a hunter of 75kg fired a bullet of 10gm at a velocity 400m/s by a 5 kg gun. if this hunters standing on iceberg then calculate it's recoil velocity​

Answer 1

Question :-

A hunter of mass 75 kg fired a bullet of 10 gm at a velocity of 400 m/s by a 5 kg gun. If this hunter is standing on an iceberg then calculate it's recoil velocity.

Solution :-

mass of hunter = 75 kg

mass of gun, m₁ = 5 kg

initial velocity of gun, u₁ = 0 m/s

final velocity of gun (recoil velocity), v₁ = ?

mass of bullet, m₂ = 10 g = 0.01 kg

initial velocity of bullet, u₂ = 0 m/s

final velocity of bullet, v₂ = 400 m/s

since,

Hunter is standing on Iceburg hence, no friction force is acting ,.also we will neglect air resistance.

it means

no external force is acting

Hence,

according to the law of conservation of momentum

initial momentum , p₁ = final momentum , p₂

Now,

using formula

momentum = mass × velocity

initial momentum, p₁ = m₁u₁ + m₂u₂

                            p₁ = 5 × 0 + 0.01 × 0

                            p₁ = 0 kg m/s

final momentum, p₂ = m₁v₁ + m₂v₂

                             p₂ = 5 × v₁ + 0.01 × 400

                             p₂ = (5 v₁ + 4)  kg m/s

so,

p₁  =  p₂

0  = 5 v₁  +  4

5 v₁ = - 4

v₁ = - 4/5 = - 0.8  m/s

Hence,

recoil velocity of gun = - 0.8 m/s

( negative sign represent that the direction of recoil is opposite to the direction of the motion (of bullet.) )