Calculus

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A hot air balloon headed due east at a speed of 20 miles per hour and at a constant altitude of 180 feet passes directly over an intersection. Find an expression for the balloon's distance d (measured in feet) from the intersection t minutes later.

  • Calculus -

    since there are 60 minutes in an hour, the speed can be expressed as 20/60 mi/min = 1/3 mi/min

    after t minutes, the distance traveled is thus t/3 miles = 1760t feet

    using a right triangle, then it is clear that

    d(t) = √(180^2 + (1760t)^2) feet

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