Question

A 16.0 kg canoe moving to the left at 12.5 m/s makes an elastic head on collision with a 14.0 kg raft moving to the right at 16.0 m/s after the collision the raft moves to the left at 14.4 m/s assuming water simulates a frictionless surface, what is the final velocity of the canoe?

Answer 1

• A 16.0 kg canoe moving to the left at 12.5 m/s makes an elastic head on collision with a 14.0 kg raft moving to the right at 16.0 m/s.
• After the collision the raft moves to the left at 14.4 m/s assuming water simulates a frictionless surface.
• Mass of the canoe (m1) = 16 Kg
• Mass of the raft (m2) = 14 Kg
• Initial velocity of the canoe (u1) = 12.5 m/s
• Initial velocity of the raft (u1) = - 16 m/s [Here, the raft's velocity is negative, because the objects are moving in the opposite direction]
• Total momentum of the system = m1u1 + m2u2 = [(16 × 12.5) + (14 × -16)] Kg m/s = (200 - 224) Kg m/s = -24 Kg m/s
• Final velocity of the raft (v2) = 14.4 m/s
• Let the final velocity of the canoe be v1.
• Total momentum of the system after the impact = m1v1 + m2v2 = [(16 × v1) + (14 × 14.4)] Kg m/s = 16v1 Kg + 201.6 Kg m/s
• According to the law of conservation of momentum, Total momentum of the system before the impact = Total momentum of the system after the impact
• or, -24 Kg m/s = 16v1 Kg + 201.6 Kg m/s
• or, -24 Kg m/s - 201.6 Kg m/s = 16v1 Kg
• or, -225.6 Kg m/s = 16v1 Kg
• or, v1 = -225.6 Kg m/s ÷ 16 Kg
• or, v1 = -14.1 m/s

Answer:

The final velocity of the canoe is -14.1 m/s or 14.1 m/s to the right.

Hope you could get an idea from here.

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