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A kite glides horizontally at an altitude of 20 m while we unspool the string. Consequently, the angle made between the string and the horizon diminishes. We would like to determine the rate at which this angle decreases once 30 m of string has been unspooled, given that, at that instant, the kite‘s horizontal velocity is 2 m/s.

To solve this problem, let θ be the angle in radians made between the string and the horizontal, x the kite’s horizontal position in meters since being attached to the ground, and t the time in seconds.

We further suppose that the string is straight and taut.

(a) Sketch a diagram of this question and use it to express θ as a function of x .

θ= Preview Change entry mode rad


(b) What is the value of x at the moment in question? Give the exact value.

x= Preview Change entry mode m


(c) What is the value of dθdt at the same moment? Give the exact value, paying attention to the sign.

dθdt=

Sagot :

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