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Homework Help: Related-rates problem

  1. Dec 8, 2015 #1
    1. The problem statement, all variables and given/known data
    A kite 100ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out? Answer: 0.02 rad/s

    2. Relevant equations

    3. The attempt at a solution
    costheta = x/200
    taking the derivative and rearranging
    theta prime= x'/-200sintheta

    substituting x' = 8 and theta = pi/6
    theta prime = -0.08 rad/s
    Last edited by a moderator: Dec 8, 2015
  2. jcsd
  3. Dec 8, 2015 #2


    Staff: Mentor

    No, this is incorrect. The height of the kite is constant, but the length of the string is not constant.
    I used ##\cot \theta = \frac x {100}## for my relationship between x and ##\theta##, and differentiated with respect to t to get the relationship between the rates.

    My work agrees with the answer you posted, except that the answer should be negative -- the angle is decreasing, which means that ##\frac{d\theta}{dt}## is negative.
  4. Dec 9, 2015 #3
    Alright makes sense thank you! I solved it
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