Question

You are with 12 other people on a boat at rest in frictionless water. The group's total mass is 936 kg , and the boat's mass is 1.2×104 kg . The entire party walks the 7.5 m distance from bow to stern.

How far does the boat move?

Answer 1

just keep the CoM of the lot at the same point and you will get the answer

Answer 2

Before they move: \[
x_{cm} = \frac{m_bx_b+m_px_p}{m_b+m_p}
\]After they move: \[
x_{cm}'= \frac{m_bx_b'+m_px_p'}{m_b+m_p}
\]If we assume that the center of mass doesn't change: \[
\frac{m_bx_b+m_px_p}{m_b+m_p}=\frac{m_bx_b'+m_px_p'}{m_b+m_p} \implies x_b-x_b'=\frac{m_p(x_p'-x_p)}{m_b}
\]