Will a light or heavier skydiver reach terminal velocity faster?

Question

And how do you prove it without using a specific example.

Answer 1

Theoretically, you never reach terminal velocity. The math is complicated but you can prove that a lighter object will reach X% of its terminal velocity sooner than a heavier object.
Solve this differential equation (it's separable): mdv/dt = mg - qv^2, then determine the effect on t when varying m. g and q are constants.

Also, common sense and experience should be sufficient: Which will reach 99% of its terminal velocity more quickly, a bowling ball or a balloon of the same size? The ballon would reach it almost immediately, while the bowling ball would take many seconds.

Answer 2

this is an interesting question, the obvious answer that first came to me was that the heavier skydiver fell faster, because the force of air drag at high speeds is equal to a function of A*v^2/m where v is the velocity, A is the area, and m is the object, i figured that the more massive you are, the smaller the drag force, and therefore the faster you fall.

however, you have to realize that the heavier you are, then the higher your terminal velocity is, since that is equal to a function of 2m/A. so it is not obviously clear whether a heavier or lighter person would reach terminal velocity faster, since the terminal velocity for the heavier person is greater than that of the lighter person.

i think the key factor is the ratio between the masses of the two skydivers and their surface areas. if the heavier person can maintain the same surface area as the light person, then the heavier person will reach terminal velocity faster. other than that generalization, its hard to say.

Answer 3

It's even more complicated than John B's description. Hidden in that qv^2 drag term is air density, which increases as you fall. I'm assuming terminal velocity is used in the sense of equilibrium velocity at any altitude. If dropped from high enough up where the air is thin, your fall speed can exceed what your TV will be further down. In that case, at some later time you will be in excess of your then-current TV and decelerate. However if not dropped from high enough you will be approaching your decreasing TV all the way down and continue to accelerate.
I do agree that the body with the larger area/mass ratio will reach TV or a certain percentage of it quicker; the bowling ball vs balloon image is compelling. But to get back to the original question, how do you prove it, I think the best argument is that since drag accel is proportional to v^2*area/mass while grav accel is constant, the body with the larger area/mass term will reach the point where drag ≈ grav with a smaller v, which implies in a shorter time.

Answer 4

True, and true of anything. Terminal velocity means as fast as something will go due to wind resistance. Since acceleration properly means a change in velocity, and there is no more change, acceleration is zero. Well, as a practical matter, you could be at terminal and then go spreadeagle and slow down, and attain a slower terminal v., and the slowing would be an acceleration on a negative vector, but that's not what you're looking for.

Answer 5

Weight is not what is important, as pointed out by the response above. Terminal velocity depends on surface area. That's how a parachute works, by replacing the relatively streamlined human body with a giant sheet of nylon that has trouble flowing through the air. If you look in your physics book, this is usually mentioned briefly (not much detail because the book wants beginning students to think in the idealized world that Galileo described) in the end of the kinematics section.

Answer 6

Terminal velocity is a function of Cross sectional area and weight. This is called 'aerodynamics'
A 30g dart will fall faster than a 30g lump of polystyrene because the air resistance is much higher for polystyrene than the dart. The dart will take longer to reach ITS terminal velocity because its terminal velocity will be MUCH higher that the polystyrene. The accelerating force (gravity) is the same for both.

Answer 7

while in a vacuum the two people will indeed reach terminal velocity at the same time the same cannot be said for two people within the real world. two people of different weights will reach terminal velocity at different times due to wind drag. therefore it can be hypothesized that a heavier person will reach terminal velocity later than a thinner person because the heavier person is larger in size causing more wind resistance ergo, more friction, drag, and less acceleration.

Answer 8

Galileo, two objects of different weight achieve same speed of falling, hit ground at same time.