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Math Help - More Differential Eqns

  1. #1
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    More Differential Eqns

    Let v(t) be the velocity, in feet per second, of a skydiver at time t seconds, t>0. After her parachute opens, her velocity satisfies the differential eqn
    dv/dt = -2v-32,
    with initial condition v(0) = -50

    b) Terminal velocity is defined as limv(t) as t approaches infinity. Find the terminal velocity of the skydiver to the nearest foot per second

    c) It is safe to land when her speed is 20 feet/second. At what time t does she reach this speed?
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  2. #2
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    Quote Originally Posted by ny_chow View Post
    Let v(t) be the velocity, in feet per second, of a skydiver at time t seconds, t>0. After her parachute opens, her velocity satisfies the differential eqn
    dv/dt = -2v-32,

    with initial condition v(0) = -50



    b) Terminal velocity is defined as limv(t) as t approaches infinity. Find the terminal velocity of the skydiver to the nearest foot per second



    c) It is safe to land when her speed is 20 feet/second. At what time t does she reach this speed?

    This equation is seperatable

    \frac{dv}{dt}=-2(v+16) \iff \frac{dv}{v+16}=-2dt

    Integrating both sides we get

    \ln|v+16|=-2t+c \iff v+16 =e^{-2t+c} \iff v(t)=Ae^{-2t}-16

    Now we use v(0)=-50=Ae^{0}-16 \iff A=-34

    v(t)=-34e^{-2t}-16

    You should be able to finish from here
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