Question

A 12 foot laddr is leaning against a vertical wall when jack beings pulling the foot ladder away from the wall at a rate of 0.2 ft/s. What is the configuration of the ladder at the instant that vertical speed of the top of the ladder equals the horzontal speed of the foot of the ladder?

Answer 1

Explanation:

Given that a 12 foot laddr is leaning against a vertical wall when jack beings pulling the foot ladder away from the wall at a rate of 0.2 ft/s

Let x be the horizontal leg and y the vertical leg

Then by Pythagorean theorem, we get

`x^2+y^2 = 12^2\\`

Differentiate to get

`2x x'+2y y'=0\\`

when both x' and y' equal to 0.2 in magnitude, we can say x'=-y'

so

x=y

The ladder will be in a position such that its height and distance of foot from base are equal.