Answer
The velocity of the boat after Batman lands on it is $+9.33m/s$
Work Step by Step
Batman has mass $m=91kg$ and velocity $\vec{v}=0$ in the horizontal direction.
He jumped onto the boat, whose mass is $M=510kg$ and has initial velocity $\vec{V}=+11m/s$.
After that, the Batman-boat system has mass $M+m=601kg$ and travels at velocity $\vec{V}_f$, which needs to be found.
We assume there are no external forces, so the total linear momentum is conserved. Therefore, $$M\vec{V}+m\vec{v}=(M+m)\vec{V}_f$$ $$\vec{V}_f=\frac{M\vec{V}}{M+m}=+9.33m/s$$
