# A man jumps on a boat at rest

1. Jun 12, 2015

### Karol

1. The problem statement, all variables and given/known data
A man of mass m is on a still boat of mass M. the man jumps to the left so he has only horizontal velocity.
Immediately afterwards the boat has velocity v.
What's the work the man made.

2. Relevant equations
Conservation of momentum: $m_1v_1=m_2v_2$
Kinetic energy: $E=\frac{1}{2}mv^2$

3. The attempt at a solution
The man's velocity, vm, in an inertial frame, after the jump:
$$Mv=mv_m\rightarrow v_m=\frac{M}{m}v$$
$$E=\frac{1}{2}\left[ Mv^2+\frac{M}{m}v^2 \right]=\frac{1}{2}\frac{M(m+1)}{m}v^2$$
I don't think it's the right answer

2. Jun 12, 2015

### DEvens

What is the square of $\frac{M}{m}v$?

3. Jun 12, 2015

### Karol

$$E=\frac{1}{2}\left[ Mv^2+m\left( \frac{M}{m}v\right)^2 \right]=\frac{1}{2}\left( M+\frac{M^2}{m} \right)v^2$$

Thanks