question 3

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 50 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 0 be the angle in radians made between the string and the horizontal, a 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 0 as a function of x . 0 = s rad (b) What is the value of x at the moment in question? Give the exact value. (c) What is the value of de dt at the same moment? Give the exact value, paying attention to the sign. de dt rad/s