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In this video you will learn how to find the Rate at which the ladder is sliding horizontally given its vertical sliding rate, height of its upper tip at time t, and its length.
A 10-foot ladder leans against the side of the building. If the top of the ladder begins to slide down the wall at the rate of 2 feet per second, 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?
0:24 Drawing & Understanding picture with given Info
2:05 Understanding what needs to be solved for - x'(t)
2:33 Finding x'(t) - Finding equation with x(t) using Pythagorean Theorem
2:56 Differentiating the found equation implicitly
3:17 Substituting known quantities into derivative equation using x(t), y(t) and y'(t)
4:24 Solving for x'(t)
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