A man jumps on a boat at rest

[Karol]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

The man's velocity, v_m, 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

 

[DEvens]

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

 

[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