Saturday, May 3, 2008

Irodov Problem 1.135

The total potential energy lost by the disc just before it leaves the surface is given by mg(H-h). This is converted into the discs kinetic energy and so if its horizontal launch velocity off the hill is given by,

The time t the disc takes before it hits the floor since it launches off is given by,

The horizontal distance traveled during this time is given by,

This is maximized when the first derivative dx/dh=0 and the second derivative is negative. It is trivial to see that this occurs at h = H/2 and the corresponding maximum distance traveled will be H.

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