A person flies a kite on the main mall. The kite rises at a rate of 2 meters per second. Suppose the horizontal distance between the person and the kite is always 6m, how fast must he release the string when the length of the string is 10 meters?
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To solve this question, we let the height of the kite be H and the length of the string be L.
The relation between H and L is: H² + 6² = L² . So when L is 10 m, the height of the kite is 8m.
Then, we differentiate both side of the equation above.
2H × H’(t) + 0 = 2L × L’(t)
H × H’(t) = L × L’(t)
L’(t) = H × H’(t) ÷ L
We are given the rising rate of the kite is 2 m/s, this means that H’(t)=2.
So, L’(t) = 8 × 2 ÷ 10 = 8/5 .