Suppose an object is dropped from height h, where h < R but gravity is not constant). Show that the speed with which it hits the ground, neglecting friction, is approximately given by:(adsbygoogle = window.adsbygoogle || []).push({});

v = sqrt(2gh)(1 - (h/2r))

where g is the acceleration due to gravity on the surface of the Earth.

HINT: You will need to expand an expression in a MacLaurin series. Be sure to expand an expression with a small value, so higher order terms can be ignored.

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# Physics Newtons Gravitation

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