A 43.0 kg parachutist is moving straight downward with a speed of 4.00 m/s .

Question

If the parachutist comes to rest with constant acceleration over a distance of 0.785  , what force does the ground exert on her?

Answer 1

1. We are ultimately trying to calculate the force of the ground on the parachutist, which means we're going to use Newton's Second Law of Motion. To be able to use that equation, we need to figure out the acceleration of the parachutist.
2. To determine the acceleration, we will use this formula:

v_f² - v_i² = 2ax

where

v_f = final velocity = 0 (the parachutist stops when he hits the ground)

v_i = initial velocity = 4.00 m/s (given)

a = acceleration

x = displacement = 0.785 m (given)

Since we are solving for acceleration, we'll move the variables around before we plug in what we know.

a = v_f²- v_i² / 2x

a = 0 - 16 / 2 (0.785) = - 16 / 1.57 = 10.19 m/s²

Well, okay, but the problem is that we know the acceleration of gravity on Earth is 9.81 m/s². So the acceleration can't be faster than that.

3. Now we can figure out the force acting on the parachutist.

F = ma

F = (43.0 kg) (9.81 m/s²) = - 421.83 N