- #1
Nirck
Hi everyone. I just began my Calculus based physics course 3 weeks ago and I really love it. I've been going ahead of the class though and came across the following problem:
As g, the acceleration due to gravity, is constant for only a limited range of height distances, a better approximation would be the linear equation
a(h) = g - hg'
where h is the distance from the ground and g' is a small constant of proportional dimensions.
My problem is that I now need to derive velocity as a function of distance, and then as a function of time.
I've tried everything I can think of, but I just can't seem to wrap my head around how I can express height as a function of time, or vice versa, without knowing either acceleration as a function of time or velocity as a function of time, but I can't get either of those without knowing one of the other two!
Any help would be greatly appreciated. Thanks in advance.
As g, the acceleration due to gravity, is constant for only a limited range of height distances, a better approximation would be the linear equation
a(h) = g - hg'
where h is the distance from the ground and g' is a small constant of proportional dimensions.
My problem is that I now need to derive velocity as a function of distance, and then as a function of time.
I've tried everything I can think of, but I just can't seem to wrap my head around how I can express height as a function of time, or vice versa, without knowing either acceleration as a function of time or velocity as a function of time, but I can't get either of those without knowing one of the other two!
Any help would be greatly appreciated. Thanks in advance.