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11 votes
11 votes
-moves "The string of a kite is perfectly taut" and always makes an angle of 35 degrees above horizontal. (a) If the kite flyer has let out 500 feet of string, how high is the kite? (b) If the string is let out at a rate of 10 feet per second, how fast is the kite's height increasing?

User Infogulch
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1 Answer

15 votes
15 votes

Answer:

a)
h=286.8ft

b)
(dh)/(dt)=5.7ft/s

Explanation:

From the question we are told that:

Angle
\theta=35

a)

Slant height
h_s=500ft

Generally the trigonometric equation for Height is mathematically given by


h=h_ssin\theta


h=500sin35


h=286.8ft

b)

Rate of release


(dl)/(dt)=10ft/sec

Generally the trigonometric equation for Height is mathematically given by


h=lsin35

Differentiate


(dh)/(dt)=(dl)/(dt)sin35


(dh)/(dt)=10sin35


(dh)/(dt)=5.7ft/s

User Ioneyed
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