# Related-rates problem

• OmniNewton
In summary, the angle between the string and the horizontal is decreasing at a rate of 0.02 rad/s when 200 ft of string has been let out. This can be found by differentiating the equation cot(theta) = x/100 and substituting x' = 8 and theta = pi/6. The answer should be negative as the angle is decreasing.

## Homework Statement

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

## The Attempt at a Solution

costheta = x/200
taking the derivative and rearranging
theta prime= x'/-200sintheta

substituting x' = 8 and theta = pi/6

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OmniNewton said:

## Homework Statement

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

## The Attempt at a Solution

costheta = x/200
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.
OmniNewton said:
taking the derivative and rearranging
theta prime= x'/-200sintheta

substituting x' = 8 and theta = pi/6