Question

Two objects of masses 100g and 200g are moving along the same line and direction with velocities of 2 ms ^-1 and 1 ms ^-1 , respectively. They collide and after the collision, the first object moves at a velocity of 1.67 ms ^-1 . Determine the velocity of the second object.

Answer 1

Mass of one of the objects, m₁ = 100 g = 0.1 kg 

Mass of the other object, m₂ = 200 g = 0.2 kg 

Velocity of m₁ before collision, v₁ = 2 m/s 

Velocity of m₂ before collision, v₂ = 1 m/s 

Velocity of m₁ after collision, v₃ = 1.67 m/s 

Velocity of m₂ after collision = v₄ 

According to the law of conservation of momentum: 

Total momentum before collision = Total momentum after collision 

m₁v₁ + m₂v₂ = m₁v₃ + m₂v₄ 

⇒ 0.1×2 + 0.2×1 = 0.1×1.67 + 0.2×v₄ 

⇒ 0.4 = 0.67 + 0.2×v₄

⇒ v4 = 1.165 m/s 

Hence, the velocity of the second object becomes 1.165 m/s after the collision.