Balistic Pendulum Velocity Approximation Formula Explanation and Solution

[Oldblood]

Homework Statement

Show that the velocity of a projectile with mass m that hits a balistic pendulum with mass M can be written as v= x*sqrt(g/L)(M+m)/m

L is the length of the sting on the pendulum and g acceleration due to gravity. x is the maximum horizontal amplitude of the pendulum. The "=" is an approximation

Homework Equations

Conservation of momentum
Conservation of energy

The Attempt at a Solution

This is what I have found:
mv=(m+M)V (conservation of momentum)

0.5(M+m)V^2 = (M+m)gh (conservation of energy)

=> V=sqrt (gh) => v= sqrt(2gh)(M+m)^2/m

V is velocity of the projectile and pendulum after the collision and h is the maximum height of the pendulum.

So it looks like I have to find h in therms of x. In my attempt using the equation of a circle i found that h= sqrt (L^2-x^2)+L

then substituting h with the x therm. Would that give me the correct answer? And I don't see how to go from here to get the approximation they want me to show

 

[VitaX]

What exactly is a balistic pendulum?

 

[Dekoy]

I tried it using angular frequency since frequency is 1/time and x/time = velocity. It seems to work but I don't know if that's the right approach. Does anyone know if that's correct or if that's possible.

 

[The legend]

What exactly is a balistic pendulum?

google it .
http://en.wikipedia.org/wiki/Ballistic_pendulum