# A person stands in a stationary canoe and throws a 5.22 kgstone with a velocity of 8.20 m/s at an angle of 34.0 degrees abovethe horizontal. The person and the canoe have a combined massof 105 kg. Ignoring air resistance and effects of the water,find the horizontal recoil velocity (magnitude and direction) of the canoe.

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A person stands in a stationary canoe and throws a 5.22 kgstone with a velocity of 8.20 m/s at an angle of 34.0 degrees abovethe horizontal. The person and the canoe have a combined massof 105 kg. Ignoring air resistance and effects of the water,find the horizontal recoil velocity (magnitude and direction) of the canoe.

2021-04-17
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.

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