Answer
The mass of the boat is $0.062kg$
Work Step by Step
We take due east to be the $+x$ direction and due north to be the $+y$ direction. We examine the collision in the x component here.
The rock, whose mass is $m=0.072kg$ and which has initial horizontal velocity $\vec{v}_{0x}=+(13m/s)\cos15=+12.56m/s$, collides with the boat, whose mass $M$ is unknown and which has initial horizontal velocity $\vec{V}_{0x}=0$.
After the collision, the rock has velocity $\vec{v_{fx}}=+(11m/s)\cos12=+10.76m/s$ and the boat has velocity $\vec{V_{fx}}=+2.1m/s$
We assume the horizontal total linear momentum is conserved. Therefore, $$M\vec{V}_{0x}+m\vec{v}_{0x}=M\vec{V_{fx}}+m\vec{v}_{fx}$$ $$0+0.9=2.1M+0.77$$ $$2.1M=0.13$$ $$M=0.062kg$$
