Applications and ExamplesSkydiving If a body of mass m
Chapter 7, Problem 77E(choose chapter or problem)
Problem 77E
Applications and Examples
Skydiving If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of the velocity, then the body’s velocity t sec into the fall satisfies the differential equation
where k is a constant that depends on the body’s aerodynamic properties and the density of the air. (We assume that the fall is short enough so that the variation in the air’s density will not affect the outcome significantly.)
a. Show that
satisfies the differential equation and the initial condition that y = 0 when t = 0.
b. Find the body’s limiting velocity,
c. For a 160-lb skydiver (mg = 160) with time in seconds and distance in feet, a typical value for k is 0.005. What is the diver’s limiting velocity?
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