Problem # p015 |

A small drop of water is released from a cloud with initially zero velocity. It's subsequent speed is determined by gravity (g=9.81 m/s²) and air resistance which is proportional to the square of the velocity : For a spherical rain drop of 6 mm ( about 1/4 inch ) diameter we have :

Force of air resistance = k * v^{2} with
k =7.35*10^{-6}[kg/m]
v = velocity [m/s]

Force of gravity : 1.1*10^{-3} [N]

- What is the terminal velocity of the rain drop ? HINT : what happens to acceleration as terminal velocity is approached ?
- Determine the equation for the speed v as function of distance y (t=0 , y=0 , v=0) HINT : don't use a=dv/dt
- Based on your equations at which distance has the drop reached 90 % of its terminal velocity ?