A raft with a mass of 180 kg carries two swimmers having masses of 50 kg and 80 kg. The raft is initially at rest. The swimmers dive off opposite ends of the raft at the same time, each with a speed of 3 m/s. At what velocity and direction will the raft move?

V = 0.5 m/s

Explanation:

Given,

Mass of the raft, M = 180 Kg

initial velocity of raft, u = 0 m/s

Final velocity of the raft, V = ?

Mass of swimmer 1, m₁ = 50 Kg

initial velocity of swimmer, u₁ = 0 m/s

Final velocity of the swimmer 1, v₁ = 3 m/s

Mass of swimmer 2, m₂ = 80 Kg

Initial velocity of the swimmer 2, u₂ = 0 m/s

Final velocity of the swimmer 2, v₂ = - 3 m/s

Using conservation of momentum

M u + m₁ u₁ + m₂ u₂ = M V + m₁ v₁ + m₂ v₂

M x 0 + m₁ x 0₁ + m₂x 0 = 180 x V + 50 x 3 + 80 x (-3)

180 V = 90

V = 0.5 m/s

Hence, the speed if the raft is 0.5 m/s in the direction of swimmer 1.