Question

Two campers dock a canoe. Once the canoe comes to rest, one camper with a mass of 80.0-kg gets off the canoe with a velocity of +4.0 m/s. The canoe and the other camper drift off in the opposite direction with a speed of 2.78 m/s. What is the combined mass of the canoe and the second camper

Answer 1

Solution :

Given :

Initially the canoe is at rest : Thus initial momentum will be zero (P_i = 0).

Mass of camper who jumps off is : m₁ = 80 kg

Velocity of camper : v₁ = 4 m/s

Velocity of canoe and other camper : v₂ = - 2.78 m/s

Let the combined mass of the canoe and the second camper be m₂.

.

Thus : Final momentum will be : P_f = m₁ v₁ + m₂ v₂

Now, According to the conservation of momentum : P_f = P_i

∴ m₁ v₁ + m₂ v₂ = 0

∴ (80 kg)(4 m/s) + m₂(- 2.78 m/s)= 0

∴ m₂ = 115 kg