Question

A ladder 20 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 π/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 π/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 π/3, find dw/dt=  

feet/sec.

Answer 1