Chapter 6159Q6.17From the proportionality of the drag force to the speed squared and from Newton’s second law, wederive the equation that describes the motion of the skydiver:mdvdtmgDAvyy=−ρ22where Dis the coefficient of drag of the parachutist, and Ais the projected area of the parachutist’sbody. At terminal speed,advdtyy==0 and VmgDAT21 2ρFHGIKJ.When the parachute opens, the coefficient of drag Dand the effective area Aboth increase, thusreducing the speed of the skydiver.Modern parachutes also add a third term, lift, to change the equation tomdvdtmgDAvLAvyyx=−−ρρ2222where vyis the vertical velocity, and vxis the horizontal velocity. The effect of lift is clearly seen inthe “paraplane,” an ultralight airplane made from a fan, a chair, and a parachute.Q6.18The larger drop has higher terminal speed. In the case of spheres, the text demonstrates thatterminal speed is proportional to the square root of radius. When moving with terminal speed, an
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