Once Kate's kite reaches a height of 52 ft (above her hands), it rises no higher but drifts due east in a wind blowing 6 ft divided by s. How fast is the string running through Kate's hands at the moment that she has released 105 ft of string?

Question

Physics

Ferguson

31 October, 09:18

Once Kate's kite reaches a height of 52 ft (above her hands), it rises no higher but drifts due east in a wind blowing 6 ft divided by s. How fast is the string running through Kate's hands at the moment that she has released 105 ft of string?

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Answers (1)

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Jairo Sweeney · Answer 1

5.213ft

Explanation:

Z² = x² + y²

x = √ (z² - y²)

y = 52ft, dx = 6ft, z = 105ft, dz = ?

d (z² = x² + y²)

2zdz = 2xdx

dz = xdx/z

But x = √ (z² - y²)

dz = √ (z² - y²) / z * dx

dz = [√ (105² - 52²) / 105] * 6

dz = √ (8521) / 17.5

dz = 5.213ft