Related Rates: AP Calculus?

a) A kite 100 feet above the ground moves horizontally at a speed of 8 feet/second. At what rate is the angle between the string and the horizontal decreasing when 200 feet of string have been let out?

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  • 1 decade ago
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    cotΘ=x/100

    x=100cotΘ

    dx/dt=100(-csc^2Θ)dΘ/dt

    dx/dt=(-100/sin^2Θ)dΘ/dt

    dΘ/dt= (-sin^2Θ/100)dx/dt

    sinΘ=100/200=1/2

    dΘ/dt=(-1/2)/100*8

    dΘ/dt=-1/25 rad/sec

    Θ is decreasing at a rate of -1/25 rad/sec

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