Conservation of linear momentum:

\(\displaystyle{\left({m}_{{{1}}}+{m}_{{{2}}}\right)}{v}_{{{i}}}={m}_{{{1}}}{v}_{{{1}{f}}}+{m}_{{{2}}}{v}_{{{2}{f}}}\)

\(\displaystyle{0}={\left({5.22}\right)}{\left({8.2}\right)}{\cos{{34}}}+{105}{v}_{{{2}{f}}}\)

Solve for \(\displaystyle{v}_{{{2}{f}}}\). The answer will be negative,meaning the velocity of the canoe will be in the direction oppositethat of the stone.

\(\displaystyle{\left({m}_{{{1}}}+{m}_{{{2}}}\right)}{v}_{{{i}}}={m}_{{{1}}}{v}_{{{1}{f}}}+{m}_{{{2}}}{v}_{{{2}{f}}}\)

\(\displaystyle{0}={\left({5.22}\right)}{\left({8.2}\right)}{\cos{{34}}}+{105}{v}_{{{2}{f}}}\)

Solve for \(\displaystyle{v}_{{{2}{f}}}\). The answer will be negative,meaning the velocity of the canoe will be in the direction oppositethat of the stone.