What is the force of air resistance acting on the sky diver, in Newtons?

Question

An 80-kg sky diver jumps from an airplane. After 8 seconds, his speed is increasing at a rate of 3.2 m/s². What is the force of air resistance acting on the sky diver, in Newtons? (Express your answer to the nearest whole number and do not include units.)

Answer 1

So a free body diagram might look like this:

Newtons second law say F = ma or, in this case ∑F_y = ma_y

The sum of the forces in the y direction is: F_{air resistance} + F_g and that equals ma_y

We also know that F_g = mg

So F_{air resistance} + mg = ma_y or F_{air resistance} = ma_y - mg

We know a_y = -3.2 m/s², we know g = -9.81 m/s², we know m = 80 kg

So:

F_{air resistance} = ma_y - mg

F_{air resistance} = 80(-3.2) - (80)(-9.8)

F_{air resistance} = -256 - (-784) = -256 + 784 = 528 (this answer is in Newtons but you are told to just give a number answer without units)