Calculating Vector Magnitude and Components | Vectors V1 & V2 Homework Help

[matt72lsu]

Homework Statement

Vector V1 is 6.4 units long and points along the negative x axis. Vector V2 is 8.9 units long and points at 60 degrees to the positive x axis
1) find x and y components of v1 and v2?
2) find magnitude of the sum v1+v2?
3) find the angle of the sum v1+v2?

Homework Equations

The Attempt at a Solution

I found the answers to part 1 (v1= -6.4,0 and v2= 4.5,7.7) and part 2 (8.0) but need help with part 3. thanks!

 

[rock.freak667]

The Attempt at a Solution

I found the answers to part 1 (v1= -6.4,0 and v2= 4.5,7.7) and part 2 (8.0) but need help with part 3. thanks!

If you have |v₁| ,v₂| and |v₁+v₂|, then you have the 3 sides of a vector triangle.


You can get the angle between v₁ and v₂, since the angles at a point add up to 180°.

Then from there you can use sine or cosine rule.

 

[matt72lsu]

im having trouble with v1+v2. i am getting -1.9 for the x component and 7.7 for the y. could i use tan-1 (y/x) = angle in this case?

 

[rock.freak667]

im having trouble with v1+v2. i am getting -1.9 for the x component and 7.7 for the y. could i use tan^-1 (y/x) = angle in this case?

using that will give the acute angle measured clockwise. use tan_-1(|y|/|x|) to get the magnitude of the angle and then 180- that angle to get it measured anti-clockwise

 

[matt72lsu]

will it matter if i use a pos 1.9 instead of a -1.9?

 

[rock.freak667]

will it matter if i use a pos 1.9 instead of a -1.9?

you will get a negative angle is all.

 

[matt72lsu]

so i got 76.1 degrees (using pos 1.9) so just 180-76.1= 104 degrees counterclockwise from the positive x axis?

 

[rock.freak667]

so i got 76.1 degrees (using pos 1.9) so just 180-76.1= 104 degrees counterclockwise from the positive x axis?

Yes that should be correct.