Related Rates: Ladder Problem

Question

A ladder 3 meters long leans against the wall of a building. The top slides down at a rate of 0.25 m/sec. How fast is the angle between the ladder and the ground decreasing when the angle is 30°?

Answer 1

Given dy/dt = -.25 m/s, find dθ/dt for ladder of length 3 m

Let's lean the ladder against a wall to the right. You want an equation for θ in terms of y. (Often you need a constraint that allows you to make the equation for θ in terms of only one variable, but, in this problem, you do not need to do this.)

sin(θ) = y/3

Take derivative implicitly in terms of t and solve for dθ/dt:by substituting in all the givens

cos(θ) dθ/dt = 1/3 dy/dt