Question

A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is k = 0.19. It can be shown that the downward velocity of the sky diver at time t is given by v(t) = A(1 − e^-kt) where t is measured in seconds and v(t) is measured in feet per second (ft/s). Suppose A = 64.
(a) Find the initial velocity of the sky diver.
(b) Find the velocity after 5 s and after 15 s. (Round your answers to one decimal place.) ...?

Answer 1

The initial velocity of the sky diver would be t=0. So put that into the equation:

v(0)=64(1−e(−0.19)(0))

and for b it will be
(5)=64(1−e(−0.19)(5)), and likewise for t=15. You just need to throw it in a calculator.