A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.3 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.)
Accepted Solution
A:
check the picture below.
so, when r = 10 and x = 8, the vertical distance is 6, namely in pythagorean theorem lingo, b = 6.
let's keep in mind that, the ladder is not growing any longer or shrinking, and therefore is constantly always just 10, that matters, since is just a scalar value and also because the derivative of a constant is 0.