Pollutants from a nearby factory are dispersed in the air from a smoke stack 200 m in the air. An individual soot particle has a terminal velocity of 1 m s-1 as it fall through the air. A wind blows horizontally with a speed of 20 m s ^-1 . How long will it take before the particle reaches the floor and how far will it have traveled?

Now imagine that the wind is no longer uniform, but varies with height. In particular, the wind speed varies as W = 1.4147 ^1/2

Where h is height and the (Hellman) exponent is taken to be ^1/2 , which corresponds to flat coastal regions. Note when the height is 200 m then the wind speed is 20 m s ^-1 , but as the height decreases the wind speed decreases. On the ground the wind speed is zero. How long will it take before the particle reaches the floor and how far will it have traveled?