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Math Help - Differentiation (2)

  1. #1
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    Differentiation (2)

    Q:

    A rocket, R, rises vertically from a point A on ground level. It is observed from another point B on the ground, where B is 10 km from A. When the angle of elevation has the value pi/4 radians, this angle is increasing at the rate of 0.005 radians per second. Find, in m/s, the velocity of the rocket at that instant.

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  2. #2
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    We must find dy/dt given x=10, \frac{d{\theta}}{dt}=\frac{1}{200}, \;\ {\theta}=\frac{\pi}{4}

    \frac{y}{10}=tan{\theta}

    Differentiate:

    \frac{dy}{dt}=10sec^{2}{\theta}\frac{d{\theta}}{dt  }

    Plug in your knowns and you're all set.
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