Repulsive central force, finding the minimum separation distance

[Smack]

Homework Statement

A particle of mass m is subject to a repulsive central force Am/r^{3} (A is a constant). At a large distance from the center of force, the particle has speed v_{0} and its impact parameter is b. Use conservation of energy and angular momentum to show that the closest m comes to the center of force is r_{min} = SQRT(b^{2} + A*v_{0}^{2}).

Homework Equations

Well, if u = 1/r, then d^{2}u/dtheta^{2} + u = -Am/[r]^{3}
and l = b*v_{0}

r= (ml^{2}/k) / (1+SQRT(1+2Eml^{2}/k^{2} cos(theta - theta_{0}) ) )

The Attempt at a Solution

I think that somehow the force is related to k, but I'm not sure. I know that the minimum value of r will be at theta equal to theta_{0} but I'm really getting confused...

 

[_coyote_]

I have the equations, but I just can't figure out how to get the minimum value of r. Any help would be greatly appreciated!