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## Homework Statement

There is a ball mass M hanging on a massless string length L, from a nail in the wall. When the ball is projected with initial horizontal velocity V, it swings up, but then falls back down and hits the nail. Find V in terms of M L and g.

**2. Requested Help**

I would appreciate it if someone could see if my method is problematic, and if my answer is correct if you would want to work it out.

## The Attempt at a Solution

For ball to leave a circle and transit to a parabolic motion, Tension in string must equal to zero at point of transition. Thereafter, the parabolic motion will coincide with the nail. I have 3 equations and 3 unknowns - velocity at moment of transition, time taken for parabolic flight, and angle from vertical which transition occurs.

Using the above, I got an angle of 65.53 deg

I got v^2 = gl cos(angle)

And I eliminated t.

Finally, after using conservation of energy, I arrive at projection velocity V = Sqrt(3.24Lg)