I was trying to solve this problem:
A ladder 13ft long is leaning against a wall. It suddenly starts to slide away at the base of the ladder. When it is 12ft away from the wall it is sliding away at 5ft/s
if it is 12 feet away then at that moment the other side is 5ft high
I found that at that moment the side on the wall is coming down at -12ft/s
What I can't find is how much the angle between the base and the ground is changing at that moment. I know it is -1 rad/s but I can't get there.
If is the angle between the ladder and the ground then where h is the height of the ladder on the wall and x is the distance from the base of the ladder to the wall.
We are told that, at this point, x= 12, h= 5, , and you have calculated that . Also so radians.
Putting all of that into the formula:
which is very close to -1.