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Rate of Change of the Angle of Elevation

  1. Nov 16, 2008 #1
    A balloon rises at the fate of 8 feet per second from a point on the ground 60 ft. from an observer. Find the rate of change of the angle of elevation when the balloon is 25 feet above the ground

    I converted 8 ft/s to 2.44 m/s2 to make it easier. I also figured the angle of elevation when the balloon was at 25 feet is around 22.6 degrees. I'm just not really sure what they're looking for. Do they want to know how many degrees the angle changes per second? If so, how do I find it? If not, what are they looking for and how do I find that?
     
  2. jcsd
  3. Nov 16, 2008 #2

    LowlyPion

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    Yes what they want is the rate of change of the angle.

    Your formula for elevation angle is

    V*t/D = tanθ

    But what is the rate of change of θ ? Isn't it the derivative of θ with respect to time?

    So Tanθ*dθ/dt = ... ?

    To find the magnitude of the change then evaluate the result at t = 25/8 seconds right?
     
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