Question

A ladder 5m long is standing vertically, flat against a vertical wall, while its lower end in on the horizontal floor. The lower end moves horizontally away from the wall at a constant speed of 1m/s while the upper end stays in contact with the wall. Find the speed at which the upper end is moving down the wall 4 seconds after the lower end has left the wall.

Answer 1

If y is the height and x is the distance from the wall, then
x^2+y^2=25
x dx/dt + y dy/dt = 0
After 4 seconds, x=4 and y=3 so,
4 * 1 + 3 dy/dt = 0
dy/dt = -4/3

so the top is sliding down the wall at 4/3 m/s