Question

A ladder 5 m long is leaning against a vertical wall. If a person pulls the bottom of the ladder away from the wall at a rate of 0.5 m/s, how fast is the top sliding down the wall when the bottom of the ladder is 3 m from the wall? V= 3

πr 2
h
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Answer 1

Let x be distance of bottom of ladder from wall

Let H be distance of floor to top of ladder

x^2 + H^2 = L^2 Pythagorean theorem

2 x dx/dt + 2 H dH/dt = 0 L is length of ladder and is fixed

dH/dt = - x/H dx/dt

x = 3 given H = 4 to complete theorem

dH/dt = -3/4 * .5 m/s = -.375 ft/sec rate of height of ladder changing