A 10 ft long ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 3 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall?

Explanation:

We are given that

Length of ladder,z=10ft

Let x be the distance of bottom of ladder from the wall and y be the distance of the top of ladder from the bottom of wall.

We have to find the rate at which the top of the ladder sliding down the wall when the bottom of the ladder is 6ft from the wall.

i.e.x=6 ft

By Pythagoras theorem

Differentiate w.r.t time

this is poiselle's equation from fluid mechanic in physics. mech eng