Question

A 20m long ladder is leaning against a wall. The top of the ladder is sliding down the wall at a constant speed of 2m/s. How quickly is the bottom of the ladder moving away from the wall when the bottom of the ladder is 5m from the wall? Give your answer as an exact expression.

Answer 1

If the top of the ladder is at height y, then

x^2+y^2=400
when x=5, y=5√15

x dx/dt + y dy/dt = 0
Now just plug in your numbers.