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DanielleElmas [232]

2 years ago

6

Once Kate's kite reaches a height of 50 ft (above her hands), it rises no higher but drifts due east in a wind blowing 7 ft d

ivided by s. How fast is the string running through Kate's hands at the moment that she has released 107 ft of string?

1 answer:

Margaret [11]2 years ago

7 0

Answer:

dz = 7.136 (answer)

Explanation:

given height for kate's kite = 50 ft (say y)

due to drift it move towards east = dx = 7 ft

string maximum length = 107 ft ( say z)

we have to find change in z

that is dz

it will form a right angle triangle for x , y and z where x is base y is height and z is hypotenuse

so we get according to Pythagoras Theorem

$z^2 = x^2+y^2\\$ ...............(i)

by derivative both side consider y as constant

$2zdz = 2xdx\\dz = {xdx }/z$

from (i) equation

$x = \sqrt{z^2-y^2}$

$dz = \sqrt{z^2-y^2}dx/z$

now put the value and find dz

$dz = (\sqrt{120^2-50^2)}7/107\\ =((\sqrt{14400 -2500} )\times7)/107$

after solving these we get

$dz =\frac{109.08\times7}{107}$

dz = 7.136 (answer)

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