Question

In the sliding ladder problem of session 31(related rates), the tutor treats the ratio of the edges as unchanging, however surely if the ladder is being pulled away, the angle it makes with the ground, and thus the ratio of the heights will not be constant?

Answer 1

You are correct that the angle the ladder makes with the ground is changing as the ladder is pulled away from the wall. However, Joel does not assume the ratio of lengths is unchanging. Quite the opposite. It is for that reason he refers to the length of the shorter hypotenuse as 20 - d, and the larger hypotenuse as 20 when determining the relation between x and y. Only after he has differentiated and found the relative rates that are true for all values does he plug in specific values to find the specific rate of decrease in height.

For anyone not taking the course, here is the question:
A 20 ft ladder leans over a 12 ft wall so that 5ft project over the wall. The bottom of the ladder is pulled away from the wall at 5ft/s. How quickly is the top of the ladder approaching the ground?
And the linked video: http://youtu.be/d484GRz9zjY

Answer 2

As Joel mentions in the video, there are several ways to solve the problem, as several parts are changing at related rates.

I'll help walk you solve the problem another way (if you like) that involves relating the rate of change in x, to the rate of change in h, height, via the rate of change in, alpha, the top angle in the similar triangles.