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Calculus

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an observer stands 200 m from the launch site of a hot-air balloon. the balloon rises vertically at a constant rate of 4 m/s. how fast is the angle of elevation increasing 30 s after the launch.

  • Calculus - ,

    tan(a) = h/200

    sec^2(a) da/dt = 1/200 dh/dt

    da/dt = 1/200 cos^2(a) dh/dt

    When t=30, h = 4*30 = 120m
    tan(a) = 120/200 = 0.6
    so, cos(a) = 0.857

    da/dt = .005 * 0.857^2 * 4 = .0147 rad/s

    That's roughly pi/68 rad/s

  • Calculus - ,

    Were you drunk when you posted this Steve?

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