Complicated maths question? Need help?

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1. A space shuttle was launched straight up, and its altitude is given by h = 10 t^2 after t seconds. You are on the ground 500 metres away from the launch site watching the shuttle going up. The line of sight from you to the rocket makes an angle x with the horizontal. By how many radians per second is x changing ten seconds after the launch?

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  • Anonymous
    8 years ago
    Favorite Answer

    h = 10t²

    Differentiate.

    dh/dt = 20t

    h = 500tan(x)

    Differentiate.

    dh/dx = 500sec²(x)

    dx/dt = dx/dh dh/dt

    dx/dt = dh/dt ÷ dh/dx

    dx/dt = 20t ÷ 500sec²(x)

    dx/dt = 20t ÷ 500(1 +tan²x)

    dx/dt = t ÷ 25(1 + tan²x)

    At t = 10, h = 1000 and 1000=500tanx so tanx = 2

    dx/dt = 10 ÷ 25( 1 + 2²) = 10 ÷ 125 = 0.08 rad/s

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