A 6 kg mass collides with a body at rest. After collision they travel together with a velocity equal

to one-third of the velocity of the 6 kg mass. Find the mass of the second body.

with calculation

12 kg

Explanation:

Momentum before collision = momentum after collision

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

After the collision, they have the same velocity, so v₁ = v₂ = v:

m₁ u₁ + m₂ u₂ = m₁ v + m₂ v

m₁ u₁ + m₂ u₂ = (m₁ + m₂) v

We know that m₁ = 6 kg, u₂ = 0 m/s, and v = u₁ / 3.

(6 kg) u₁ + m₂ (0 m/s) = (6 kg + m₂) (u₁ / 3)

(6 kg) u₁ = (6 kg + m₂) (u₁ / 3)

6 kg = (6 kg + m₂) (1/3)

18 kg = 6 kg + m₂

m₂ = 12 kg