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

1. ## 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!

2. 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.

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

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

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

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

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

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:

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

I will let you take it from there.

3. "High School and Pre-University Math Help"

Thats what this is.

Thanks.

4. 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