An 81 kg stuntman jumps from the top of a building 29 m above a catching net. Assuming that air resistance exerts a 100 N force on the stuntman as he falls, determine his velocity just before he hits the net
In order to solve this, we can get all tangled up in acceleration,
or we can just add up the energy budget.
-- Gravitational potential energy = (mass) (grav accel) (height above something)
-- 29 m above the net, his potential energy is (81 x 9.8 x 29) = 23,020 joules
-- All the way down, air resistance exerts 100 N of force against him.
The energy burned up by air resistance is the work done = 100 x 29 = 2,900 joules.
-- The energy he has left when he hits the net is (23,020 - 2,900) = 20,120 joules.
-- When he hits the net, all of his energy is kinetic energy . . . (1/2) (m) (v²)
(1/2) (m) (v²) = 20,120
(40.5) (v²) = 20,120
v² = 20,120 / 40.5
v = square root of (20,120 / 40.5) = 22.3 meters per second (about 50 mph)