Another Word Problem

[Annie493]

A kite 100 ft above the ground moves horizontally at a speed of 3 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out? (Enter your answer as a fraction)

 

[Deleted member 4993]

A kite 100 ft above the ground moves horizontally at a speed of 3 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out? (Enter your answer as a fraction)

Please show us your work, indicating exactly where you are stuck - so that we may know where to begin to help you

 

[galactus]

Here's a shove. Always make a diagram. They help.

Find the angle marked by @ on the diagram by using basic trig (the angle is \(\displaystyle {\theta}\), but Paint does not have that so I am reserved to using @).

You can also use Pythagoras to find the length of x.

Relate x to the angle: \(\displaystyle cot({\theta})=\frac{x}{100}\)

Now, differentiate w.r.t time and solve for \(\displaystyle \frac{d\theta}{dt}\)

Let us know what you get.