Skydiving If a body of mass m falling from rest under the action of gravity cncounters an air resistance proportional to

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Skydiving If A Body Of Mass M Falling From Rest Under The Action Of Gravity Cncounters An Air Resistance Proportional To 1 (52.88 KiB) Viewed 14 times

Skydiving If a body of mass m falling from rest under the action of gravity cncounters an air resistance proportional to the square of the velocity, then the body's velocity t sec into the fall satisfies the differential equation dv m = mg - kv² dt where k is a constant that depends on the body's acrodynamic properties and the density of the air. (We assume that the fall is short enough so that the variation in the airs density will not affect the outcome significantly.) a. Show that V = ( √ Th mg Vụ tanh k satisfies the differential equation and the initial condition that v = 0 when t = 0.