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A ladder 23 feet long leans against a wall and the foot of the ladder is...

A ladder 23 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of ?/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.)

(a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is ?/3, find dh/dt=  feet/sec.

(b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is ?/3, find dw/dt=  feet/sec.

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Answer #1

xdistance faom tbase of [addes, z- distance along laddes that fie hasclimed 23 feet h ? height distance from wall thetaefghes ? angle ot base of laddest Girn the laddes is sliding away at a canstanta3 Jeet Sec mefightes, is climbing uk ladde9 at a sate of ? feet/sec i9t C dt I dx -Sine - d? dt 23 sine dt 3 2 d t 23 sin T dt 233 23 Sin (o) - dh, at z= 6 at 6323J3 ? = 2.3 23 dt CoS?? 23-Z 23-2 cosse d? dt 3 dt- 23 dt d26 d? 23

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Answer #2

刀 b: H-23 * ingataf(3.day) A.Heast f:3ft 2 2t to. : 141. - 19.92 ce- 2

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