Rates Of Change

Calculus Level pending

A ladder AB of length 5 m has one end A leaning against a vertical wall. The other end B rests on the horizontal ground. When A is at a height of 4 m, it slides down the wall at the rate of 2 m/s. How fast is the other end, B,sliding along the horizontal ground? (Give your answer in 3 significant figures?)


The answer is 2.67.

Daniel Kua by Daniel Kua , 20, Canada

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1 solution

Daniel Kua
Nov 29, 2015

Let x = distance from base of the ladder to the wall at time t y = height of ladder above the ground at time t

Given: dy/dt = -2 Find: dx/dt when y = 4

Solution: The triangle formed by the ladder, wall, and ground is a right-angled triangle. 

              By the Pythagorean Theorem, x2 + y2 = 25

              Differentiate implicitly with respect to t to get

                    2x(dx/dt) + 2y(dy/dt) = 0

                    dx/dt = -y(dy/dt)/x  = -4(-2)/x  = 8/x

                        Since x2 + y2 = 25 and y = 4, x = 3

                    So, dx/dt = 8/x = 8/3 meters/sec
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