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calculus

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a rocket is launched vertically and travels at 100 meters per second. a tracking radar is 500 meters from the launch site. when the rocket is 800 meters high, how fast must the radar antenna tilt( in radians) in order to track the rocket?

  • calculus - ,

    Make a diagram showing the height h, the horizontal distance 500 m and the the angle Ø.

    tanØ = h/500
    h = 500 tanØ
    dh/dt = 500 sec^2 Ø dØ/dt

    when h = 800
    the hypotenuse = 100√89
    and sec^2 Ø = 89/25

    100 = 500(89/25) dØ/dt
    dØ/dt = 25(100)/(500(89)) = 5/89 or appr .0562 radians/sec

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