A ladder 6m long rests against the vertical wall. How far is the top of the ladder sliding down the wall when the bottom of the ladder is 4m from the wall and sliding at a speed of 1m/s?

Answer 1

let the height along the wall be y m
let the distance from the wall along the ground be x

x^2 + y^2 = 6^2
2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0

when x = 4
16 + y^2 = 36
y = √20 , and dx/dt = 1

4(1) + √20 dy/dt = 0

dy/dt = -4/√20 m/sec

the negative shows that y is decreasing, (the ladder sliding down)