Free Falling Body

sajid_at_umerji.fsworld.co.uk
Date: 02/15/05 

Date: 15 Feb 2005 13:24:32 -0800

Suppose I drop a ball from a height h, what will the height of the ball
be at time t ?

I know how to calculate the solution under the assumption that the
acceleration is constant and equal to g.

But I'm trying to find the solution where the acceleration is equal to:

-GM/x^2

Where x is the height of the ball and M is the mass of the Earth.

Also, to simplify things, I'm assuming the ball does not have any
gravitational effect on the Earth.

I can see that:

v^2/2 = GM (1/x - 1/r)

And therefore that:
                        ___
(1/x - 1/r)^-1/2 dx = \/2gm t

But I don't know how to calculate the integral on the left hand side
...

I would appreciate some help.

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