Answer to Question #97922 in Classical Mechanics for Jake

Question

On a hot summer afternoon, Keith and Nate are out fishing in their rowboat when they decide to jump into the water and go for a swim. Keith, whose mass is 65.0 kg, jumps straight off the front of the boat with a speed of 2.00 m/s relative to the boat, while Nate propels his 68.0-kg body simultaneously off the back of the boat at 4.00 m/s relative to the boat. If the 100.-kg boat is initially traveling forward at 3.00 m/s, what is its velocity after both boys jump?

Answer 1

From the conservation of momentum:

$$(m_K+m_N+M)v=m_Kv_k+m_Nv_N+MV$$

$$(65+68+100)3=(65)2-(68)4+100V$$

$$V=8.41\frac{m}{s}$$

Direction: forwards.