A falling skydiver has a mass of 101 kg. What is the magnitude of the skydiver's acceleration when the upward force of air resistance has a magnitude that is equal to one-fourth of his weight?

Explanation:

When the skydiver is falling towards the ground, there are two forces acting on him:

- The force of gravity, downward, of magnitude , where

is the mass of the skydiver

is the acceleration due to gravity

- The air resistance, upward, of magnitude

The net force on the skydiver must be equal to the product between mass and acceleration, so we can write:

where a is the acceleration.

Here we are told to find the acceleration of the skydiver when the magnitude of the air resistance is 1/4 of his weight, which means

Substituting into the equation and solving for a, we find the acceleration:

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