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

Answer:

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

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