Solve Ball Swinging Problem with Different Formulas and Calculations

[ianbearpig]

I'm having trouble figuring out this problem. I'm not sure what equations to use or how to start it, can anyone help??

1. A ball is attached to a string (extentionless and massless, of course) of length L. The string is attached to a frictionless pivot point. When the string is vertical, the ball is a distance h above the horizontal ground. The ball and string are released from rest at an angle θ1 from vertical (θ1 < 90°) and the string is straight. You may place a sharp knife somewhere so that it cuts the string and allows the ball to launch. Derive a formula for the desired angle from vertical θ2 (in terms of the given variables and possibly other constants) for the following situations:

Maximum launch speed

Maximum landing speed

Maximum horizontal launch distance as measured from a location below the ball and string when they hang vertically

Maximum horizontal launch distance as measured from the launch point

Maximum launch height as measured from the ground

Maximum launch height as measured from the launch point

Calculate the above numerically when L = 2.00 m, h = 0.50 m, and θ1 = 40°.

I'm guessing it has something to do with conservation of energy. How would I use those equations to derive formulas for these scenarios?

 

[ianbearpig]

I talked to a friend and he says I should come up with the equations for each situation then take the derivative of each of those equations. Does this sound right?

 

[LawrenceC]

For the first question (maximum launch speed), where does the ball have the least potential energy yet is still attached to the string? When it has the least potential energy, what can you say about kinetic energy and velocity?