A 9.5 kg dog takes a nap in a canoe and wakes up to find the canoe has drifted o

Question

A 9.5 kg dog takes a nap in a canoe and wakes up to find the canoe has drifted out onto the lake but now is stationary. He walks along the length of the canoe at .50 m/s RELATIVE TO THE WATER, and the canoe simultaneously moves in the opposite direction at .15 m/s. What is the mass of the canoe?

I know this is a momentum problem. My question deals with the relative to the water part. If the dog were moving .5 m/s relative to the water, wouldn't he actually be moving at .15+.50 m/s in the boat? I know I am wrong, but I just want to know why I'm wrong.

Explanation / Answer

It's a momentum question. Conservation of momentum says that the dog's change in momentum is equal to the canoe's change in momentum (but in the opposite direction).

Mv (dog) = Mv (canoe)
9.5 * 0.5 = 0.15 * x

x= 31.67 kg is the mass of the canoe

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