Please help with the following Calculate the terminal velocity for a pollen grai

Question

Please help with the following

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 pm and a density of 0.7 g/cm^3. If this grain is released from the top of a tree (height 9 m), estimate the time It will take to fall to the ground. 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/m^3.) Use the exact values you enter in previous answer(s) to make later calculation(s). Calculate the drag force on a bullet that is 5.0 mm in diameter and moving at a speed of 614 m/s. Assume the drag force on the bullet is given by the equation F_drag = 1/2 p Av^2.. If the mass of the bullet is 10 g, compare this force to the weight of the bullet (w_B). Estimate your weight (W). Compare this force to your own weight, (use your estimate) A boy pushes a 2.1-kg book against a vertical wall with a horizontal force of 41 N. What is the minimum coefficient of friction that will keep the book in place without sliding?

Explanation / Answer

F = 1/2 rho v^2 A Cd

v = sqrt (2F/rho A Cd) = sqrt (2mg/rho A Cd)

mg = 4/3 pi r^3 x d x g

mg = 4/3 x 3.14 x (5 x 10^-6)^3 x 700 x 9.8 = 3.6 x 10^-12

A = 4 x 3.14 x (5 x 10^-6)^2 = 3.14 x 10^-10

v = sqrt (2 x 3.6 x 10^-12/1.3 x 3.14 x 10^-10 x 0.47) = 0.194 m/s

HEnce, v = 0.194 m/s

(for Cd = 1 ; v = 0.133 m/s)

t =d/v = 9/0.194 = 46.4 s

Hence, t = 46.4 s

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