College Algebra

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 0.23. It can be shown that the downward velocity of the sky diver at time t is given by
v(t) = 180(1 − e−0.23t)
where t is measured in seconds and v(t) is measured in feet per second (ft/s).
(a) Find the initial velocity of the sky diver

(b) Find the velocity after 5 s and after 10 s. (Round your answers to one decimal place.)
after 5 s = ft/s
after 10 s = ft/s

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  1. Are you sure? The air resistance is more like proportional to velocity square.

    However it does not matter since you do not need to know.

    v(0) = 180 * (1- e^0) but anything to the 0 is 1
    so
    v(0) = 180 (1 - 1) = 0

    v(5) = 180(1 - e^-1.15) = 180(1-.317)
    = 123

    v(10) = 180 (1 - e^-2.3) =180(1-.100)
    = 162

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