Displacement, Center of Mass

Question

A student of mass 75 kg is in a small rowboat of mass
95 kg resting on a calm lake. How far will the boat move
if the student walks from the bow to the stern of the
boat? The distance from the bow to the stern is 2.5 m.
Ignore any horizontal force exerted by the water.

 

What are the steps to solve this kind of problem?

Answer 1

M = mass of boat = 95 kg

m = mass of student = 75 kg

Δx = distance student moves = 2.5 m

 

The mass of the student shifts by Δx, so there is a first moment change mΔx.  The mass of the boat has to shift by Δx' to balance this, since the position of the center of mass will not change in this problem.  Therefore, the first moment change of the boat is

 

MΔx' = -mΔx

 

Δx' = -(m/M)Δx

 

Just plug in the numbers.