Solve Vector Problems: a + b, a - b, a - 2b

[Darkiekurdo]

Homework Statement

We have two vectors: one with a speed of 3 m/s to the northwest, let's call this vector a, and we also have a vector b moving to the west with a speed of 5 m/s.

Determine: a + b, a - b and a - 2b

Homework Equations

I have no idea.

The Attempt at a Solution

I tried to put the vectors in terms of unit vectors, but that didn't work, then I tried to use Pythagoras' Theorem, but that wasn't right either. I'm getting really frustrated with this problem!

 

[mjsd]

you need a coordinate system so that you can put vectors into component form
a = ( , ) ; b = ( , ) then addition becames simple. so first determine a set of axes and then give your vectors the appropriate coordinates before moving on. shall need some simple trig I think

 

[Darkiekurdo]

Could you show me how to do this?

 

[HallsofIvy]

Basically, what you just said you tried. Since you don't show how you tried, I don't know why it "didn't work".

"one with a speed of 3 m/s to the northwest, let's call this vector a, and we also have a vector b moving to the west with a speed of 5 m/s."
Okay, so $\vec{a}$ has equal $\vec{i}$ and $\vec{j}$ components except that the $\vec{i}$ component is negative. Set it up as a right triangle with legs x and x, hypotenuse of length 3. Use the Pythagorean theorem to determine x. The vector is $-x\vec{i}+ x\vec{j}$.

b is due west with "length" 5 so it should be easy to write it in $x\vec{i}+ y\vec{j}$ form!

Once you have those two, the arithmetic is simple.

 

[mjsd]

Could you show me how to do this?

ok, let me give u an example.

take the N direction as your +ve y-axis direction and E as your +ve x-axis direction. then a velocity vector pointing at S with magnitude 2m/s has a vector form based on this set of coord sys of
v=(0,-2)
and for a velocity vector pointing at say SW with magnitude $$\sqrt{2}$$ m/s has
u=(-1,-1)

 

[Darkiekurdo]

I'm sorry I didn't show how I did it, but I don't have internet right now. I will show how I did it when I have internet.

 

[Kurdt]

As everyone else has said you need to find the components of the vectors and then the calculations are fairly easy. In this situation south-north will be the y-axis and west to east will be the x-axis of a cartesian coordinate system. The unit vectors will then be $\mathbf{\hat{i}}$ and $\mathbf{\hat{j}}$. You know the magnitude of the vectors so you can work out the components.

$$|\mathbf{a}|=\sqrt{x^2+y^2}$$

For vector a you know that the x and y components must be the same and for vector b you know the y component is 0.

Post your attempt when you get a chance.