Answer
a) $v_{cm}=0$
b) The raft moves in the opposite direction from the sunbather.
Work Step by Step
a) At start, because both the sunbather and the raft are stationary, $v_{cm}=0$
Because we consider the sunbather and the raft as an isolated system, the principle of linear momentum conservation applies. Therefore, while she is walking, $v_{cm}$ is always constant and equals $0$.
b) The sunbather has mass $m$ and velocity $v$ while the boat has mass $M$ and velocity $V$.
$$\frac{MV+mv}{M+m}=v_{cm}=0$$ $$MV+mv=0$$ $$V=-\frac{m}{M}v$$
Because $p_{sunbather}=mv\ne0$, $V\ne0$. In other words, the raft itself moves while she is moving.
The negative sign shows the raft moves in the opposite direction of the sunbather.
