Vectors & Physics: Questions Answered

[Rhine720]

I've been going along in this physics book and I've been getting along in it. Vectors took me some time though, and i sitll have questions. So i understand how a vector "displacement" and be gained from a bunch of distances travelled, and i know the <x,y> components would simply be total east and total north traveled. But then Velocity vectors throw me off. If you're going say 30 degree North of East, then does that mean you're going X amount in the east direction and y amount in the north direction? Also, when you're in a boat crossing a river and you're going east to west at a speed, and the river is going north to south at some speed, can you pretened those are actually <x,y> component of the resultant, which will be the actual direction and speed you travel due to the effects of both the river and your own speed?

 

[BogMonkey]

I'm only learning myself too but I think I can answer this. Your idea is correct. For example say the velocity vector is 15m/s 20degrees West of North. The car or whatever is traveling in that north of west direction at 15m/s. All velocity is is unit of displacement per unit of time so the x component tells you the displacement per time in purely the West direction (this depends on whether you call the x-axis North/South or West/East of course) which will obviously be less than the velocity in the actual direction the cars goin (20degrees west of north).

In the boat example the velocity of the river has absolutely no effect on the velocity of the boat since the boat is traveling in a direction perpendicular to the current hence the vectors do not add or subtract to each other. So yeah you could make a triangle out of these velocity vectors and make the velocity of the boat and river the opposite and adjacent sides (component vectors) and the hypotenuse would be larger because the distance traversed in the south west direction (of your example) would be greatest.

Sorry if that's a crap explanation that's the first physics question I've ever answered on this forum.

 

[Rhine720]

Why would it be longer? So the components of velocity aren't speed? The compnents of displacement are distance... Sorry, I'm still a little bit confused

 

[espen180]

The components of the velocity vector represent your speed along the different coordinate axes. You are free to call these "north and east", "x and y" or something completely different. Your total speed is the length of the velocity vector.

In the case of traveling at 15 m/s at an angle 30 degrees "north" of the "east" axis, the components of the velocity vector would be 15m/s*sin(30^o)=7.5m/s along the "north" axis and 15m/s*cos(30^o)=12.99m/s along the "east" axis.

In your example wit the boat, if we assume that the boat travels with the water, then the velocity of the water can be added to the velocity of the boat with respect to the water to get the total velocity of the boat.

 

[Rhine720]

The components of the velocity vector represent your speed along the different coordinate axes. You are free to call these "north and east", "x and y" or something completely different. Your total speed is the length of the velocity vector.

In the case of traveling at 15 m/s at an angle 30 degrees "north" of the "east" axis, the components of the velocity vector would be 15m/s*sin(30^o)=7.5m/s along the "north" axis and 15m/s*cos(30^o)=12.99m/s along the "east" axis.

In your example wit the boat, if we assume that the boat travels with the water, then the velocity of the water can be added to the velocity of the boat with respect to the water to get the total velocity of the boat.

So I was correct? It didn't travel with it. They were perpendiculer to one another..

 

[espen180]

Let's say that the velocity of the boat with respect to the water is [0,b] and that the water has a velocity [a,0] and that the boat travels with the water. In the frame where the water has a velocity [a,0], the boat then has a velocity [a,b].

 

[BogMonkey]

Heres a diagram
http://img19.imageshack.us/img19/6586/diagramqq.jpg
in that picture the boats traveling north from one side of the river to the other at 2m/s. This is the y component.

The rivers current is dragging the boat West down river at 3m/s. x component.

The overall vector represents the velocity of the boat moving in that North West direction and its velocity is obviously greater than either of the components because its a combination of speed the boats traveling at by itself and the added speed the rivers current gives the boat.

 

[espen180]

Right. $$v=|\vec{v}|=\sqrt{v_x^2+v_y^2}$$

If either v_x or v_y are nonzero, then v>v_x,v_y

 

[Rhine720]

Alright thanks.. My thoughts were all correct. The diagram said exactly what i did in my first post kinda(i don't even remember what was in my first post..but yeah) Thanks guys