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.)

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.)

anonymous · Answer

it seems to be differentiation problem :| lemme try it

anonymous · Answer

The initial velocity of the sky diver would be t=0. So put that into the equation: $$v(0) = 64(1-e^{(-0.19)(0)})$$

anonymous · Answer

what about question (b)

anonymous · Answer

Same thing:$$v(5) = 64(1-e^{(-0.19)(5)})$$, and likewise for t=15. You just need to throw it in a calculator.