I am getting approximalte half what the answer should be (Related Rates Problem)

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November 7th 2009, 10:38 AM
s3a

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I am getting approximalte half what the answer should be (Related Rates Problem)

I am having trouble with this question but I believe it's a small mistake because I get approximately half of what the answer should be. I attached my work.

Question: "A ladder 10 ft long leans against a vertical wall. If the bottom of the ladder slides away from the base of the wall at a speed of 2 ft/s, how fast is the angle between the ladder and the wall changing when the bottom of the ladder is 6ft from the base of the wall?

Answer: 1/4 rad/s

Any help would be greatly appreciated!
Thanks in advance!
November 7th 2009, 10:45 AM
skeeter

Quote:

Originally Posted by s3a

I am having trouble with this question but I believe it's a small mistake because I get approximately half of what the answer should be. I attached my work.

Question: "A ladder 10 ft long leans against a vertical wall. If the bottom of the ladder slides away from the base of the wall at a speed of 2 ft/s, how fast is the angle between the ladder and the wall changing when the bottom of the ladder is 6ft from the base of the wall?

Answer: 1/4 rad/s

Any help would be greatly appreciated!
Thanks in advance!

let $\theta$ = angle between the ladder and the wall

$\sin{\theta} = \frac{x}{10}$

$\cos{\theta} \cdot \frac{d\theta}{dt} = \frac{1}{10} \cdot \frac{dx}{dt}$

$\frac{8}{10} \cdot \frac{d\theta}{dt} = \frac{2}{10}$

$\frac{d\theta}{dt} = \frac{2}{10} \cdot \frac{10}{8} = \frac{1}{4}$ rad/s
November 7th 2009, 12:30 PM
s3a

So my mistake was that SINE is what determines "THE ANGLE BETWEEN THE LADDER AND THE WALL?" Also, I now see the ladder is a constant and the x is not. Thanks.
November 7th 2009, 12:34 PM
skeeter

Quote:

Originally Posted by s3a

So my mistake was that SINE is what determines "THE ANGLE BETWEEN THE LADDER AND THE WALL?"

I don't know ... I don't do downloads on public message forums anymore.
November 7th 2009, 12:57 PM
s3a

Oh, well thanks still but if you didn't know, choosing to open rather than save pdf files would just store them into the hard drive temporarily.