Question

A ladder 29 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=

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=

Answer 1

Question:
Does the firefighter clim up 2 ft/sec along the length of the ladder , or 2 ft/sec vertically ?

Answer 2

I think we can safely assume that the firefighter's progress is measured along the ladder.

Answer 3

a) dh/dt= 1.373695468

Answer 4

A) (23*sqrt3)/29 ***when the ladder is 29 feet long
B) got stuck on this one still