Question

A ladder 12 meters long is leaning against the wall of a building. The bottom of the ladder is sliding away from the wall at the rate of 1.5 m/s. How fast is the top of the ladder sliding down when it is 3 meters above the ground?

Express your answer in square root form. Include unit of measurement.

Answer 1

Almost every Calculus textbook I have seen has a variation of this
question as one of the examples to introduce "Rates Of Change"

foot of ladder from wall ---- x m
height of ladder up the wall ---- y m

x^2 + y^2 = 12^2
2x dx/dt + 2y dy/dt = 0
given: dx/dt = 1.5 m/s
find : dy/dt when y = 3

x^2 + 3^2 = 12^2
x = √135

sub into 2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0
√135(1.5) + 3dy/dt = 0
dy/dt = -1.5√135/3 = ..... m/s