Question

A pole that is 3060 feet long is leaning against a retaining wall. The bottom of the pole is getting farther from the wall at a rate of 3 ft/sec. How fast is the top of the pole moving down the wall when the top is 1296 feet from the ground?

Answer 1

h² + b² = 3,060²

b = √(3,060² - 1,296²) = 2,772

2h(dh/dt) + 2b(db/dt) = 0

1,296(dh/dt) + 3(2,772) = 0

dh/dt = -8,316/1,296 = -6 5/12 ft/sec

= -6 ft. 5 in./sec