A kit is 100 ft high. There are 260 ft of string out and it is being let out at a rate of 5 ft/sec. If this results in the kite being carried along horizontally, what is the horizontal speed of the kite?
I know that dh/dt is 5 ft /sec and I know I have to use the Pythagorean Theorem but I'm not sure what to do from here.
I know that dh/dt is 5 ft /sec and I know I have to use the Pythagorean Theorem but I'm not sure what to do from here.
1 Answer
5.42 ft/sec
Explanation:
Let's assume the kite is flying away relative to the kite player, not to the ground. This is a better approach because the speed of the kite player is not given.
Let
Approximate the relationship between x, y and L by an right angle triangle, thus:
Take derivative with respect to time to get the speeds
where
The relationship between kite speed and string releasing rate is thus:
Solve the kite speed