Question

From a rifle of mass of 5 Kg, a bullet of mass 100g is fired with initial

velocity 50m/s. Calculate the initial recoil velocity of rifle?​

Answer 1

Given :

• Mass of rifle, m₁ = 5 kg
• Mass of bullet, m₂ = 100 g = 100/1000  kg = 0.1 kg
• Initial velocity of Rifle, u₁ = 0  [since, it will be at rest initially ]
• Initial velocity of Bullet, u₂ = 0  [since, it will be at rest ]
• Final velocity Bullet with which it is fired, v₂ = 50 m/s

To find :

• Final velocity of rifle with which it will recoil, v₁ = ?

Knowledge required :

• Law of conservation of momentum

This Law states that for an isolated system of collision between two bodies the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

• m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

[ Where m₁ and m₂ are masses of two bodies with initial velocities (velocities before collision) are u₁ and u₂ and final velocities (velocities after collision) are v₁ and v₂ ]

Solution :

Using the Law of conservation of  momentum

→ m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

→ ( 5 ) ( 0 ) + ( 0.1 ) ( 0 ) = ( 5 ) v₁ + ( 0.1 ) ( 50 )

→ 0 + 0 = 5 v₁ + 5.0

→ - 5 = 5 v₁

→ v₁ = -1 m/s

Therefore,

• Recoil velocity of Gun will be 1 m/s in the direction opposite to the direction of motion of Bullet.

Answer 2

Answer:

Given :

Mass of rifle, m₁ = 5 kg

Mass of bullet, m₂ = 100 g = 100/1000  kg = 0.1 kg

Initial velocity of Rifle, u₁ = 0  [since, it will be at rest initially ]

Initial velocity of Bullet, u₂ = 0  [since, it will be at rest ]

Final velocity Bullet with which it is fired, v₂ = 50 m/s

To find :

• Final velocity of rifle with which it will recoil, v₁ = ?

Knowledge required :

Law of conservation of momentum

This Law states that for an isolated system of collision between two bodies the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

[ Where m₁ and m₂ are masses of two bodies with initial velocities (velocities before collision) are u₁ and u₂ and final velocities (velocities after collision) are v₁ and v₂ ]

Solution :

Using the Law of conservation of  momentum

→ m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

→ ( 5 ) ( 0 ) + ( 0.1 ) ( 0 ) = ( 5 ) v₁ + ( 0.1 ) ( 50 )

→ 0 + 0 = 5 v₁ + 5.0

→ - 5 = 5 v₁

→ v₁ = -1 m/s

Therefore,

Recoil velocity of Gun will be 1 m/s in the direction opposite to the direction of motion of Bullet.