Calculate the terminal velocity for a pollen grain falling through the air using

Question

Calculate the terminal velocity for a pollen grain falling through the air using the drag force equation. Assume the pollen grain has a diameter of 10 µm and a density of 0.3 g/cm3.
_______m/s

If this grain is released from the top of a tree (height 11 m), estimate the time it will take to fall to the ground. Hint: The pollen grain will reach its terminal velocity very quickly and will have this velocity for essentially the entire motion. Your answer will explain why pollen stays in the air for a very long time. (Assume the density of air to be 1.3 kg/m3.)

Explanation / Answer

NOTE : YOU ARE NOT GIVE DRAG COEFFICIENT Cd

Your equation appears to be missing the drag coefficient for a sphere .. (Cd) = 0.47

Fd = *area*v^2*Cd/2
Fg = mg
Thus mg = *area*v^2*Cd/2 ==> v = sqrt(2mg/(*area*Cd))

F = ½ (.v².A.cd) = mg .. .. .. v = (2mg / A.cd )
--------------------------------------...
mg= (4/3.r³ x D x g)
mg = 4/3.([5^10-6m]³ x [0.30*103 kg/m³] x 9.80) = 15.386*10-13 kg

A = r² .. .. A = (5*10-6)² .. .. A = 7.85*10-11 m²

v = {(2 x1 5.386*10-13) / (1.30kg/m³ x 7.85*10-11 x 0.47)}

v = 0.24346 m/s

If I re-work the answer omitting (cd)[ or using (cd) = 1] .. I get v = 0.1144 m/s ..
.. but I believe this to be the incorrect use of the drag equation

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