A kit is 120m high and 130 m of string is out. If the kite is moving away horizontally at the rate of 52 m/sec, find the rate at which the string is being paid out.

Explanation

To solve the problem of finding the rate at which the string is being paid out when a kite is flying at a height of 120 meters and moving horizontally at a rate of 52 m/sec, we can use the Pythagorean theorem and differentiation. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a kite flying at a height of 120 meters, and the length of the string (hypotenuse) is 130 meters. The kite is moving horizontally away from the point directly below it at a rate of 52 m/sec. We need to find the rate at which the string is being paid out (the rate of change of the string length).

### Step 2: Set Up the Relationship
Let:
- \( h = 120 \) m (height of the kite)
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