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Math Help - speed calculation

  1. #1
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    speed calculation

    An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane is 10 miles away (s=10) the radar detects the distance s is changing at a rate of 240 miles per hour. What is the speed of the airplane?
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  2. #2
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    Quote Originally Posted by jimmyp View Post
    An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane is 10 miles away (s=10) the radar detects the distance s is changing at a rate of 240 miles per hour. What is the speed of the airplane?
    Let the horizontal distance of the plane be x at time t.

    s^2 = x^2 + 6^2 .... (1)

    \Rightarrow 2s \frac{ds}{dt} = 2x \frac{dx}{dt}

     \Rightarrow \frac{dx}{dt} = \frac{s}{x} \cdot \frac{ds}{dt} .... (2)

    Use equation (1) to solve for x when s = 10. You're given \frac{ds}{dt} = 240 miles per hour when s = 10 miles. Substitute all this into equation (2).
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