Math Is Fun Forum

Reuel

Member

Registered: 2010-11-28

Posts: 178

Sailboat Drag

Hello. I have been working various problems and I think I am doing alright. I am not sure what to do with this one, however.

"A sailboat is running along a straight course and under a light wind at 1 m/sec. The wind wuddenly picks up, applying a constant force of 600 N onto the boat. The only other force that is acting on the boat is water resistance where k=100 N-sec/m that is proportional to the velocity of the boat. The mass of the boat is 50 kilograms. First find an equation for the motion of the sailboat, then determine its limiting velocity under these wind conditions."

Here is what I have so far: Ft is the total force on the boat, Fw is the force of the wind, Fr is the resistance on the boat by the water, k is the proportionality of the water resistance, m is the mass of the boat, v(t) is the velocity of the boat.

Looking it up, I find that acceleration is the force divided by the mass (right?) so...

How does that look so far? Am I heading in the right direction? What does N-sec/m mean, anyway?

Reuel

Member

Registered: 2010-11-28

Posts: 178

Re: Sailboat Drag

Oops... almost forgot about this problem. I get that that limiting velocity is 6m/sec. Did anyone else work this problem out?

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Sailboat Drag

Hi Reuel,

Is this your answer too:

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Reuel

Member

Registered: 2010-11-28

Posts: 178

Re: Sailboat Drag

Hi gAr,

I believe so. I have this:

If I am understanding your question.

Last edited by Reuel (2011-03-09 05:34:16)

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Sailboat Drag

Hi Reuel,

I'm not so sure whether it can be done that way.
First find the equation for the velocity. Then the limiting velocity is the velocity it attains as t->∞, which is 6 m/s.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Reuel

Member

Registered: 2010-11-28

Posts: 178

Re: Sailboat Drag

So I understand, you are saying that the fact I got the same answer as you is a coincidence?

I'll work it out your way and see what I get.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Sailboat Drag

Yes, at least that's what i think!
Use the fact that acceleration is rate of change of velocity when deriving the equation

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Sailboat Drag

hi Reuel,

I agree with gAr in post #3.  Then as t tends to infinity, v tends to 6.

Your method for calculating 6 is not correct and you were just lucky to get the same value.

Because Newtons = k x velocity the units of k are N / (m/s) = N sec/m so the term you didn't understand is just the correct units for k.  As everything is in the 'right' units (ie. we don't need to change from metres to Km or t into hours etc) you can leave N sec/m out of your equations completely just as you should leave out the N etc.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob