- #1
d.smith292
- 29
- 0
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 1.0 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?
So, I'm having a difficult time figuring out related rates. I have grasped derivatives just fine, but developing the diagram and labeling seem to be my problems.
I’ve set up my graph like this:
http://www.flickr.com/photos/23826260@N04/8520534293/ by d.smith292, on Flickr
θ is my changing rate in this problem. I've set my equation up like this :
x = 8ft
x' = 1ft/sec
cosθ = x/10
When I differentiate the problem I get
-sinθ = 1/10(x')
When I input this into my calculator I get some crazy long decimal answer, like -.1001674212 Where am I going wrong. I've probably got the entire thing wrong. I'm having trouble with this section. I appreciate the help.
So, I'm having a difficult time figuring out related rates. I have grasped derivatives just fine, but developing the diagram and labeling seem to be my problems.
I’ve set up my graph like this:
http://www.flickr.com/photos/23826260@N04/8520534293/ by d.smith292, on Flickr
θ is my changing rate in this problem. I've set my equation up like this :
x = 8ft
x' = 1ft/sec
cosθ = x/10
When I differentiate the problem I get
-sinθ = 1/10(x')
When I input this into my calculator I get some crazy long decimal answer, like -.1001674212 Where am I going wrong. I've probably got the entire thing wrong. I'm having trouble with this section. I appreciate the help.