Monday, July 28, 2014

Miley Cyrus and Math, what the..?

Using some trigonometry, the height h is determined.

h = l - l cos (theta) where l is the length of the string (say 10 meters) and the starting angle theta (60 °).

In this pendulum system, the height h is equal to l - l cos (theta).

The energy is conserved, so the kinetic energy  E c   of the ball moving at the impact point is equal to the potential energy we have calculated (the air friction is neglected).

E c  = ½ mv 2  = mg (l - l cos (theta))

This allows to derive the speed v at which the ball hits the wall.

v = sqrt (2 gl (1-cos (theta))) = sqrt (2 x 9.81 x 10 (1 - cos (60 °)) is v = 9.904 m s -1

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