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**Conservation of Energy - "Swing Problem"**

Hi everyone I'm having some trouble solving this problem because I'm not sure what method to use. It seems like it could involve Centripetal acceleration, conservation of energy, and/or conservation of momentum.

**Problem**

A swing seat of mass M is connected to a fixed point P by a massless cord of length L. A child also of mass M sits on the seat and begins to swing with zero velocity at a position at which the cord makes a 60° angle with the vertical is shown in Figure I. The swing continues down until the cord is exactly vertical at which time the child jumps off in a horizontal direction. The swing continues in the same direction until its cord makes a 45° angle with the vertical as shown in Figure II: at that point it begins to swing in the reverse direction. With what velocity relative to the ground did the child leave the swing? (cos 45° = sin 45° = , sin 30° = cos 60° = 1/2, cos 30° = sin 60° = /2)

**Diagram**

http://img222.imageshack.us/img222/4968/phys1rp6.jpg

So far, I figured you could use the conservation of energy formula

Pe1+Ke1=Pe2+Ke2 to determine velocity in terms of L

Ke1 cancels out when the swing is at rest and Pe2 cancels out when the swing is vertical.

mgh = 1/2mv^2

( I wasn't sure if Pe2 should include the mass of the second person or not)

This is assuming the person jumped off

(2m * 9.8m/s^2 * L-Lcos60) = (1/2 * m * v^2)

18.6L m/s = v^2

This is if the person is still on the swing

(2m * 9.8m/s^2 * L-Lcos60) = (1/2 * 2m * v^2)

9.8L m/s = v^2

I tried a few things from here - using centripetal acceleration and angular momentum formulas but nothing worked out. I'm not sure if I'm even starting it right.

Thanks for any help & I'm still a high school student so I may not understand some terminology or if I'm even doing the math right (sorry for that)

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