# Related-rates problem

1. Dec 8, 2015

### OmniNewton

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

Last edited by a moderator: Dec 8, 2015
2. Dec 8, 2015

### 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.

3. Dec 9, 2015

### OmniNewton

Alright makes sense thank you! I solved it