Assume you want to make a parachute jump. You know that you can change the air r

Question

Assume you want to make a parachute jump. You know that you can change the air resistance by giving the air a bigger or smaller cross section to resist. But you are curious about what influence your body weight has on the maximum speed you can reach: You know that the driving force pulling you down to earth is m g. Furthermore you also know that the air resistance is a function that increases with increasing velocity (and area). (If you are not convinced of this, drive your car at different speeds and put your hand out of the window!) Finally you remember that the maximum speed is the speed when there is no more acceleration (i.e. the force pulling you down and the force pulling you up are equal). With all this knowledge, try to explain why a heavy body can reach a higher maximum velocity than a light one (given that they have the same shape and size). (If you want to use an equation for the air resistance you can d.g. use F(upsilon) = const upsilon^2 which is true in some limit.)

Explanation / Answer

Maximum velocity is obtained when gravitational force equals air resistance force.

mg = const*v2

v = (mg/const)

So more mass means higher maximum velocity. Therefore, heavier object have higher maximum velocity than lighter object.

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