Suppose there is a 10 meter ladder leaning against the wall of a building and the base of the ladder is sliding away from the building at a rate of 3 meters per second. How fast is the top of the ladder sliding down the wall when the base of the ladder is 8 meters from the wall?

Answer 1

The ladder is the hypotenuse of a right triangle, with the sides being the ground and the wall.

By Pythagorean Theorem, a^2 + b^2 = c^2. c, the length of the ladder, is constant. Take b to be the ladder's height on the wall, and a the distance on the ground from the wall.

Differentiate with respect to time.
2a(da/dt) + 2b(db/dt) = 0

db/dt = -(a/b)(da/dt)

When the base of the ladder is 8m from the wall, c = 10 so b = 6 by Pythagorean Theorem. da/dt is given as 3m/s; find db/dt.