Understanding Relative Velocities: Solving a Simple Vector Question

[Mo]

I have just today revised over simple vetors.I have attempted a few questions, however there is one which, although i worked out the answer for (kind of a fluke!) , i still don't actually understand how/why.

ok the question is:

"One ship sails due south at 7 m/s while another sails due east at 4m/s .What is the velocity of the second ship relative to the first?

I drew out a simple vector diagram with a horizontal and vertical component (its called component right?) and worked out the resultant.The resultant was "square root of (16+49)" .This is 8.06 m/s

I don't understand what i have actually worked out though.What do they actually mean by "relative velocities", if this wasnt in the vectors section of the book, i would have just tried to work out a ratio like 4:7 !

Thanks

Regards,
Mo

 

[dextercioby]

When u compose 2 vectors,what mathematical operation u do to them??

HINT:For relative velocities,it's the "reverse" operation.

Daniel.

 

[Mo]

eh? sorry i don't understand what you mean.

Do you mean "combine" vectors?
in that case we would use pythagoras theorem to find the resultant/sum?

Mo

 

[dextercioby]

I didn't use the word "combine",but "compose"...

In this case u need to subtract one vector from the other (u figure out which is to be subtracted) and,indeed,use pythagorean thorem to find the modulus...

Daniel.

 

[Mo]

Oh man! modulus? - I am guessing that what you call the number left.

(im only a few months into the course!) nevermind, thanks for your help anyway.

Regards,
Mo

 

[dextercioby]

Oh man! modulus? - I am guessing that what you call the number left.
(im only a few months into the course!) nevermind, thanks for your help anyway.

How do you expect solving problems involving vectors,if u don't know what a vector is?? "Modulus" is a word which appears in the definition of a vector.The "physical" definition...

Daniel.

 

[Mo]

Hmm that's strange, cause modulus does not appear anywhere in the vetcors section of my textbook.

in fact the definition for the vector is (in my textbook):

"Quanitites which have both magnitude and direction are called vectors" ... "the simplest ways to tackle vector problems is to start with a vector diagram .."

hmm .. no "modulus" word used ...

the main problem i was having was with understanding how we could use vectors to solve the question above, and what "relative velocities" exactly meant.

I think it would be better to ask my teacher, as he could draw the diagram is well.

Thanks for your help anyway.

Regards,
Mo

 

[DaVinci]

Relative Velocities basically is referring to the various velocities as seen from one reference frame or another. The first reference frame you are talking about, call it S, is probably a dock or a stationary observer not in either boat. To keep matters simple, consider him to be at the starting point of each ship. Hence the 4m/s and 7m/s.

Now, your next frame of reference, call it S` (S Prime) is on the first boat. He does not see himself as moving (disregard physical representations of movement such as water going by and such) because he is at constant velocity. But he sees the stationary observer and the other boat as moving away. So, with him moving south at 7m/s, how fast is the second boat receeding from him (what does he measure the velocity of the second ship to be (pretend he has a radar gun))?

The magnitude of the ship is going to be the square root of the sum of all the force vectors... u' = sqrt(ux^2, uy^2, uz^2) where x, y, and z are subscripts.

Now you just need to find what to plug in for each of the u forces. The last hint I will give is that on a 3d plane, uz is going to be 0 since there is no difference in the ships 'altitude'.

 

[dextercioby]

Hmm that's strange, cause modulus does not appear anywhere in the vetcors section of my textbook.
in fact the definition for the vector is (in my textbook):
"Quanitites which have both magnitude and direction are called vectors" ... "the simplest ways to tackle vector problems is to start with a vector diagram .."
hmm .. no "modulus" word used ...

What?? Sorry,but i have to ask you,coz it's a question that's haunting me:what grade are you in??Are u in HS??

Daniel.

 

[DaVinci]

How do you expect solving problems involving vectors,if u don't know what a vector is?? "Modulus" is a word which appears in the definition of a vector.The "physical" definition...
Daniel.

Funny, the first time I actually heard the word modulus being referred to a vector was in a Complex Variables course. It is normally referred to as 'magnitude'.

Instead of busting on the guy because his vocabulary is different from yours (not his fualt.. it would be the teachers or the books), how about explaining it more clearly for him...

 

[Mo]

Yes.I have just started AS level there. And all 3 of my textbooks do not mention modulus.

Regrads,
Mo

PS: Thank you Davinci for your explanation and help. And yes, the word they use in the textbooks is "Magnitude"

 

[dextercioby]

Yes.I have just started AS level there. And all 3 of my textbooks do not mention modulus.

Regrads,
Mo

Take this problem as a positive part:you have learned that for vectors,"modulus=magnitude".This is really weird,as in my first year of HS (the 9-th grade),i was taught that vectors are "animals" which have:
*origin (bonded vectors);
*direction (the line which is a support for them on which they can move freely,if they don't have origin/are not bonded);
*sensen that line they must have a sense (the sense of the arrow=direction in which the arrow points);
*a modulus.Intuitively,how long the arrow which denotes a vector is...

Daniel.

PS.I guess textbooks in England suck,big time...

 

[DaVinci]

PS.I guess textbooks in England suck,big time...

Most of the time they have the same textbooks that we do except they pay 1/4 what we do for them. Thank our government for that one.

I am in my junior year at a University after having gone through all of my schooling in America as an American. The first time I heard modulus referred to as the magnitude of a vector was this week in Applications of Complex Variables (a math course).

Looking back, just to prove a point, in my Calculus 1, 2, & 3 and Physics 1 & 2 book, it is also referred to as magnitude and not modulus. Looking through my Physics 3 book, guess what it is called? Magnitude. Engineering Statics book... front cover... magnitude. Statics in the entire chapter dealing with learning vectors... magnitude. Intro to Theoretical Methods... magnitude. Every book I have, all American textbooks bought in America and written by academic Americans... all say magnitude.

Now if you are done insulting him and the textbooks in his country due to a vocabulary word that you some how picked up that the rest of the world hasn't, then we can move on and stop playing games.

 

[dextercioby]

Now if you are done insulting him and the textbooks in his country due to a vocabulary word that you some how picked up that the rest of the world hasn't, then we can move on and stop playing games.

I'm not an American,i'm a Romanian.I've been taught physics and maths in Romania.I did't insult him,but the authors who made those textbooks...They didn't tell them what a vector is,what it does and what terminology is being used for its various atributes...That is just awful...

Daniel.

 

[HallsofIvy]

"modulus"= "magnitude"= "length" (although, strictly speaking, "length" only applies to vectors between two points).

"magnitude" applies to any kind of vector.
For velocity vectors, "magnitude" is the same as "speed".

The "relative velocity" between two boats is the rate at which the straight line distance between them is changing, together with the direction between them.

In this problem you can think of one vector as pointing east with "magnitude" 4 and the other pointing south with "magnitude" 7. The straight line distance between the boats is the hypotenuse of a right triangle with legs of length 7 and 4 and so the length of the hypotenuse is $\sqrt{7^2+ 4^2}= \sqrt{49+ 16}$ as you say.

 

[DaVinci]

I did't insult him,but the authors who made those textbooks...
Daniel.

Then you are insulting a whole lot of books...