ladder and how fast the bottom moves

Question

A  foot ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of  feet per second, how fast is the bottom moving along the ground when the bottom of the ladder is  feet from the wall?

Answer 1

Length of ladder: L , x: dist from foot of ladder to base of wall , y: vert. dist from top of ladder to base of wall

dx/dt: s ft/sec , dy/dt = ?

x² + y² = L²

2x·dx/dt + 2y·dy/dt = 0

dy/dt = -x/y·s and since y = √(L² - x²). dy/dt = - (x · s) / √(L² - x²).