A 10-foot ladder leans against the side of a building. If top of ladder begins slide down ...

Question

A 10-foot ladder leans against the side of a building. If the top of the ladder begins to slide down the wall at a rate of 2 ft/sec. how fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 8 feet off the ground?

Answer 1

This scenario forms a right triangle with the hypotenuse being the length of the ladder. Let x be the horizontal direction and y be the vertical direction.

dy/dt = -2 ft/s as given. (Negative since it is sliding down)

x²+y²=10²

Taking the derivative of both sides of the equation

2xdx/dt + 2ydy/dt = 0

dx/dt = -y/x dy/dt

When y = 8, x = √(100-64) = 6

dx/dt = -(8/6) (-2) = 8/3 ft/s