(a) At high Reynolds number, the drag force on a moving object becomes largely independent of the viscosity of the fluid. Given that the drag force in this case is a function of the fluid density, the object size R, and its speed v, use dimensional analysis to obtain a formula for the drag force.
(b) From a sheet of paper, cut out two circles, one with a radius twice as large as the other, and using scissors and some Scotch tape turn them into two cones as shown in Figure 12.22(A). Stand on a chair and drop the two cones from the same height, pointy end down, as shown in Figure 12.22(B). You will observe that after a short period, both cones reach a terminal speed. Which cone is moving faster? Explain your observation based on the formula derived in (a). (Hint: Derive a formula for the terminal speed as a function of the cone size by balancing the drag force and the force of gravity.)