Let's say there's a creek.(adsbygoogle = window.adsbygoogle || []).push({});

Down in the creek, there is a current.

The vector field that describes this current is

Cur[x y z]= [(ðy)^x]i+ [(y^4)+(xyz)]j+ (2z + e^z)k

Nota bene:

ð = pi

The force is in Newtons.

X, Y, and Z are the spatial dimensions in meters, whose origin is a piece of bait in this case.

You see, there's also this guy who's fishin' in the creek. His bait's down there, situated on the origin.

A fish sees it, and circles around it one complete time. The fish is unsure during this period, and maintains a distance of one meter.

This motion takes exactly 2ð seconds for the fish.

So, the motion can be described as a vector-valued function of t, time (sec.)

Fis(t)= [cos(t)]i+ [sin(t)]j+ [0]k

How much work is done by the fish?

Ok... so I made this problem up... that's why it's so weird. :)

I need help setting it up. I know I need to use a line integral.

The upper limit, t, in seconds, will be 2ð, while the lower will obviously be 0.

So, first off, I need to find the integrand, which is the dot product ofCur[Fis(t)]andFis'(t).

To begin

Cur[Fis(t)]= [(ð*sin(t))^cos(t)]i+ [sin(t)^4]j+ 1k

But here's some trouble for me... I'm not certain on how to differentiateFis(t).

Tell me, O somebody-who-is-doubtlessly-wiser-than-I, would

Fis'(t)= [-sin(t)]i+ [cos(t)]j+ 0k?

If that is so, I'll continue to find the dot product, and then begin the actual integration.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# How much work does the fish do?

**Physics Forums | Science Articles, Homework Help, Discussion**