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,
[tex]a^{2} + 300^{2}= c^{2}[/tex]
when y = 500
[tex]a^{2} + 300^{2}= 500^{2}[/tex]
a = [tex]\sqrt{500^{2} - 300^{2}}[/tex]
= 400
thus
[tex]a^{2} + 300^{2}= c^{2}[/tex]
2a da/dt = 2c dc/dt
a da/dt = c dc/dt
400 (25) = 500 dc/dt
dc/dt = 1000/500
= 20 ft/s
