Gravity and Terminal Velocity: Understanding the Relationship

[curtmorehouse]

Newbie question here, so sorry if it is silly to those in the know..

If a skydiver reaches his terminal velocity because the drag caused by air at height x, why isn't the gravity at x/2 strong enough to overcome the already reached terminal velocity? It seems to me that a falling object would reach terminal velocity for the gravity and drag at that point in the fall (x), but ever increasing gravitational pull should overcome the previously experienced drag.

Like if I jump out of a plane with a parachute, my terminal velocity will be N. But if I jump out with a parachute and a 100 lb weight strapped to my body, I'll fall faster, ie. have a greater terminal velocity. Thre greater weight causes an acceleration through the terminal velocity N to the new terminal velocity W. Isn't relative gravity like adding weight for decreasing distance from an object?

 

[tiny-tim]

Welcome to PF!

If a skydiver reaches his terminal velocity because the drag caused by air at height x, why isn't the gravity at x/2 strong enough to overcome the already reached terminal velocity? It seems to me that a falling object would reach terminal velocity for the gravity and drag at that point in the fall (x), but ever increasing gravitational pull should overcome the previously experienced drag.

Hi curtmorehouse! Welcome to PF!

In principle, you're right about x/2 …

but (you knew there was a "but", didn't you? ) the percentage difference in distance from the Earth's centre is so small that the terminal velocity would be increased by a factor of less than .0001.

(of course, if you fall far enough, the difference will become noticeable … but it will be more than canceled by the increase in air density, and therefore in air resistance! )

 

[jtbell]

Just to clarify tiny-tim's point, in case curt isn't aware of this... the gravitational force on an object depends on the distance from the center of the earth, not on the distance from the ground. The radius of the Earth is 6378 km, so if you fall from a height of 5 km to 1 km, your distance from the center of the Earth changes from 6383 to 6379 km, a difference of about 0.06%.