Calculus

Derivatives - chain rule

An airplane, flying horizontally at an altitude of 1 mile, passes directly over an observer. If the constant speed of the airplane is 400 miles per hour, how fast is its distance from the observer increasing 45 seconds later? Hint: note that in 45 seconds (3/4 * 1/60 = 1/80), the airplane goes 5 miles.

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  1. the distance z is found using

    z^2 = 1^2 + x^2
    at x=5, z^2 = 26

    z dz/dt = x dx/dt

    so at the moment in question

    √26 dz/dt = 5*400

    note that z will be in mi/hr

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