Answer to Question #101394 in Physics for Nyx

Question

A 106 kg man sits on the stern of a 5.7 m long
boat. The prow of the boat touches the pier,
but the boat isn’t tied. The man notices his mistake, stands up and walks to the boat’s
prow, but by the time he reaches the prow,
it’s moved 3.4 m away from the pier.
Assuming no water resistance to the boat’s
motion, calculate the boat’s mass (not counting the man).
Answer in units of kg. Don't round answer.

Answer 1

The position of the center of mass will not change during the motion of the man.

$$x_g=\frac{106(5.7)+ma}{106+m}$$

$$x_g=\frac{106(3.4)+m(a+3.4)}{106+m}$$

$$106(3.4)+m(a+3.4)=106(5.7)+ma$$

$$m=72\ kg$$