Question

From a rifle of 4kg a bullet of mass 0.01kg is fired with a velocity of 35 m/s calculate the recoil velocity of a rifle ?

Answer 1

ANSWER :-

Recoil velocity of rifle = - 0.0875 ms⁻¹

(where negative sign shows that rifle will recoil in the direction opposite to the motion of bullet)

EXPLANATION :-

→ mass of bullet , m₁ = 0.01 kg

→ initial velocity of bullet , u₁ = 0  (because bullet is initially at rest)

→ velocity with which bullet is fired , v₁ = 35 ms⁻¹

→ mass of rifle , m₂ = 4 kg

→ initial velocity of rifle , u₂ = 0  (because rifle is initially at rest)

→ and Let, recoil velocity of rifle = v₂ = ?

Using formula to calculate momentum

momentum = mass × velocity

Calculating initial and final momentum of bullet

initial momentum of bullet = m₁ × u₁

initial momentum of bullet = 0.01 × 0

initial momentum of bullet = 0

final momentum of bullet = m₁ × v₁

final momentum of bullet = 0.01 × 35

final momentum of bullet = 0.35 kg ms⁻¹

Calculating initial and final momentum of rifle

initial momentum of rifle = m₂ × u₂

initial momentum of rifle = 4 × 0

initial momentum of rifle = 0

final momentum of rifle = m₂ × v₂

final momentum of rifle = 4 × v₂

Using the law of conservation of momentum

Law of conservation of momentum is stated as : In a collision between two bodies the total momentum of two bodies before collision is equal to the total momentum of bodies after collision.

so,

↦ total momentum initially = total momentum finally

↦ initial momentum of bullet + initial momentum of rifle = final momentum of bullet + final momentum of rifle

↦ 0 + 0 = 0.35 + ( 4 × v₂ )

↦ 0 = 0.35 + 4 v₂

↦ - 0.35 = 4 v₂

↦ v₂ = - 0.35 / 4

↦ v₂ = - 0.0875 ms⁻¹

Hence,

Recoil velocity of rifle will be -0.0875 ms⁻¹  .

( negative sign represent that rifle will recoil in direction opposite to motion)