Question

A girl flies a kite at a height of 500 ft, the wind carrying the kite horizontally away from her at a rate of 20 ft/sec. How fast must she let out the string when the kite is 700 ft away from her? ft/sec

Answer 1

she must let out the string when the kite is 700 ft away from her at 20 ft/s

Step-by-step explanation:

given information:

a = the distance between the girl

b = the length of the string

a = 300

da/dt = 20 ft/s

c =500 ft, dc/dt = ?

Pythagorean Theorem,

`a^(2) + 300^(2)= c^(2)`

when y = 500

`a^(2) + 300^(2)= 500^(2)`

a =
`\sqrt{500^(2) - 300^(2)}`

= 400

thus

`a^(2) + 300^(2)= c^(2)`

2a da/dt = 2c dc/dt

a da/dt = c dc/dt

400 (25) = 500 dc/dt

dc/dt = 1000/500

= 20 ft/s