# Object falling with non-constant gravity

The exact problem reads: The acceleration of gravity g is a constant only for a limited
range of height differences. A better approximation, one that
might hold over a larger range of height differences, is that g decreases
linearly with height, g = go - hg', where h is the
height measured from the ground surface and s' is a (small) constant
of the appropriate dimensions. (a) Find the speed of a
dropped object as a function of height assuming it was dropped
starting from rest from a height ho. (b) Find the speed of
a dropped object as a function of time assuming it was dropped
starting from rest from a height ho.

What I've tried to do so far for part a was to integrate acceleration in terms of h. I'm not sure if that is even allowed, but I ended up getting v = g0h - 0.5g'h^2

Then on part b, I more or less got stuck trying to get a formula for h in terms of t, and I'm not quite sure where to start.

I may just be thinking about this incorrectly, so any input on the best method for starting this problem would be welcome.

Related Introductory Physics Homework Help News on Phys.org
rl.bhat
Homework Helper
At any instant, acceleration is given as
g = dv/dt= dv/dh*dh/dt = v*dv/dh = go - hg'
Now find the integration to find v in terms of h.
Now g = go - hg' = go + ( ho - 1/2*gt2)g'
Collect the terms containing g and write g = ......
Then write g = dv/dt and find the integration to find v in terms of t.

Last edited: