What is the speed of a wedge sliding down an inclined plane?

[Identity]

Homework Statement

A point particle of mass m is sliding down a wedge inclined at an angle of $$\alpha$$ to the horizontal. The wedge has a mass m and is free to slide on a smooth horizontal surface. When the mass has fallen a height h, what will be the speed of the wedge?

Homework Equations

The Attempt at a Solution

I tried a kinematics approach with a lot of angle-bashing and eventually came up with:

$$v = \frac{h}{g^2} \cot \alpha$$

But this is wrong, and I have a feeling this is too complex for kinematics

I've thought about a conservation of energy approach with

$$mgh = \frac{1}{2}mu^2+\frac{1}{2}mv^2$$

where 'u' is the speed of the particle and 'v' is the speed of the block, but I don't know how to divde up the speeds!

thanks

 

[ideasrule]

Have you tried the conservation of momentum? There's no external forces in the x direction, so horizontal momentum must be conserved.

 

[Identity]

Thanks, I hadn't considered conservation of momentum, I think I've got it now