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A gymnist is swinging on a high bar. The distance between his waist and the bar is 1.1M. At the top of the swing his speed is momentarily zero. ignoring friction and treating the gymnist as if all his mass is located at his waist, find his speed at the bottom of the swing.

At the bottom of his swing, he has lost gravitational potential energy
PE = 2 M g * 1.1 m

If all his mass were at his waist, the velocity of the waist would be given by

KE = (1/2)M V^2 = 2 M g * 1.1 m,
because the potential energy loss would be cnverted to kinetic energy.
Cancel out the unknown M and solve for V.

V = sqrt (4*g*1.1 m)

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