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Calculus 1 relative rates question

  1. Oct 11, 2013 #1
    1. The problem statement, all variables and given/known data

    An airplane flies at an altitude of 8 miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates at which the angle of elevation θ is changing when the angle is θ = 30°, θ = 60°, and θ = 80°.

    3. The attempt at a solution

    I tried solving this problem by my self but i kept getting stuck at one the same spot every time.



    sec^2(θ) * dθ/dt = 8/x^2 * 600

    and that's as far i get every time and i don't know if I'm doing it right or not.
  2. jcsd
  3. Oct 11, 2013 #2


    Staff: Mentor

    Makes more sense to call the plane's velocity dx/dt. Also, since the plane is flying toward the observer, x is decreasing, so dx/dt < 0.
    d/dt(8/x) = d/dt(8x-1) = -8x-2 * dx/dt
    Notice that the right side represents a positive number if x > 0.

    Other than that, your equation of the rates looks fine. Now solve for dθ/dt, and evaluate it at the three given values of θ. Don't forget to convert the angles to radians.
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