Newton's third law question

Question

A 57.2 kg girl steps out of a 4 kg canoe. In doing so, she pushes the canoe backwards, accelerating the boat at 1.2 m/s/s. Determine the magnitude of the girl's acceleration.

Answer 1

Set the magnitude of the force (F = ma) on the girl equal to the magnitude of the force on the empty canoe, and get the acceleration of the girl from that.

M = mass of empty canoe (given)

m = mass of girl (given)

a₁ = magnitude of acceleration of canoe (given)

a₂ = magnitude of acceleration of girl = ?

Ma₁ = ma₂

a₂ = Ma₁ / m

You know M, a₁, and m. Plug in the numbers and get a₂ in m/s². The direction of the girl's acceleration will be opposite to the direction of the canoe's acceleration.