Answer to Question #157462 in Physics for Hilario Encarnacion

Question

Determine the center mass of the fisherman and boat system if the fisherman stands at the end of a boat length L. The fisherman has a mass ¼ of the boat when is at rest.

Answer 1

The center of mass of the boat itself is at its center. The center of mass of the man is where he is. The center of mass of this system can be found with a simple equation (assuming that zero coordinate is at the boat's front):

$$x_c=\frac{m_bx_b+m_fx_f}{m_b+m_f},\\\space\\ x_c=\frac{M\cdot(L/2)+(M/4)(L)}{M+M/4}=0.7L.$$

The center of mass is at a distance of 0.7 L from the front of the boat.