Question

You stand 40ft from a bottle rocket on the ground and watch as it takes off vertically into the air at a rate of 20ft/sec. Find the rate at which the angle of elevation changes when the rocket is 30 ft in the air Consider the function f(x) = a. Find an interval where the Rolle's Theorem applies. Explain how the conditions are met. b. Name an interval where the Mean Value Theorem does not apply. Explain how the conditions are violated.

Answer 1

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PAGE: 23412 1 20ft/sec. A toft B I A is the position of person who stand 40 ft (AB) from a bottle rocket on the ground and watching when it takes off vertically into the air at the rate of 20 ft/sec. de 04 = 20 ftsec.be dt Let the angle of elevation ý o it gn ABC. tano = BC - AB - . y = you x 40 ut tano - 40 Differentiating with respect to t- dly a (dane). - d ( 2 ) tano a dt at 40 - Coso) ds I seco do e dox 201 t sec²o. do a cos²o dt, 20 when, y = 30ft, using Pythagoras theorem- AC² = AB & B c² E 40²+30² = 2500

DATE: PAGE: AC= 50 ft Now, wars OD 8- Coso = AB = 40. = 4 - AC 503 = woso at when yg when y=30 - 16/25 = 2 16 25x2 25 - 0.32 rad/sec Hence, the rate at which the angle of elevation changes when the socket is 30 ft in the air a I do at do - 0.32 rad's -