Particles of plant pollen are often nearly spherical, with diameters ranging from about 10 to 100 m

Particles of plant pollen are often nearly spherical, with diameters ranging from about 10 to 100 μm and densities of about 1000 kg/m³. Suppose that a sudden gust of wind dislodges such particles and lifts them to a height of 5 m, followed by a steady breeze at 4 m/s.

(a) Calculate the terminal velocities for two sizes of pollen, D = 10 and 100 μm.

(b) Assuming that the terminal velocity is reached immediately, how far will each be carried before reaching the ground?

(c) Confirm that for both particle sizes the time needed to attain the terminal velocity is negligible.