Could I get some help finding the rate of an angle changes

• Mar 9th 2009, 05:36 PM
Meeklo Braca
Could I get some help finding the rate of an angle changes

A fish is being reeled in at a rate of 30cm/s from a bridge 4m above water. At what rate is the angle (in rad/s) between the line and the water changing when there is 8m of line out?

Thank You!
• Mar 10th 2009, 11:46 AM
sinewave85
Quote:

Originally Posted by Meeklo Braca

A fish is being reeled in at a rate of 30cm/s from a bridge 4m above water. At what rate is the angle (in rad/s) between the line and the water changing when there is 8m of line out?

Thank You!

This is a problem which requires the use of the differential and therefore belongs on the calculus thread. That said, here is how to solve it.

http://i125.photobucket.com/albums/p...athdraw2-1.jpg

First we set up an equation that describes the relationship between the constants and variables:

$\sin{\theta} = \frac{4}{D}$

$\theta = \arcsin{\left(\frac{4}{D}\right)}$

then we differentiate that equation to put it in terms of rates:

$\frac{d \theta}{dt} = \frac{1}{\sqrt{1 - (\frac{4}{D})^{2}}}\left(\frac{-4}{D^{2}}\right)\frac{dD}{dt}$

That equation describes the general situation. In your example, the specific situation is when the "fish is being reeled in at a rate of 30cm/s" and "there is 8m of line out." So:

$D = 8$ and $\frac{dD}{dt} = -0.3 m/s \mbox{(negative because the distance is decreasing)}$

I will let you take it from there.
• Mar 10th 2009, 11:59 AM
Meeklo Braca
"High School and Pre-University Math Help"

Thats what this is.

Thanks.
• Mar 10th 2009, 12:43 PM
sinewave85
Quote:

Originally Posted by Meeklo Braca
"High School and Pre-University Math Help"

Thats what this is.

Thanks.

I sense hostility in those terse declaratives. I really wasn't trying to chastize you. The thing is that solving this problem requires a concept, the derivative, that is by definition a calculus concept, whether you are taking the course in highschool or college -- and if you are taking in in highschool, good for you. With problems that require calculus concepts, you are probably better off putting them on the calculus thread here:

http://www.mathhelpforum.com/math-help/calculus/

where people who know how to tackle these kinds of problems are more likely to see them.

One of the mods makes the same point:

http://www.mathhelpforum.com/math-he...questions.html