A kite 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 step by step, we will use the relationship between the height of the kite, the horizontal distance from the kite to the person holding the string, and the length of the string itself. We will apply the Pythagorean theorem and differentiate with respect to time.

### Step-by-Step Solution:

1. **Define the Variables:**
- Let \( h \) be the height of the kite, which is given as \( h = 120 \) m.
- Let \( x \) be the horizontal distance from the person to the point directly below the kite.
- Let \( y \) be the length of the string, which is given as \( y = 130 \) m.
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