Problem # 034 |

A sky-diver (mass = m = 80 kg) jumps out of a ballon
( initial velocity = v_{0} = 0 , initial location y=0).
As she falls
air resistance exerts a force on her which increases quadratically
according to :

F_{air} = k * v^{2}
k = 0.25 N / (m/s)^{2}

- Starting with a clean free-body diagram develop an equation for the sky-diver's velocity as function of distance fallen. Observe that the integrand of the integral to be solved has a numerator which is the derivative of denominator.
- For the given data determine the velocity after the sky-diver has fallen 300 m and 3000 m.