Calculating Displacement with Vectors

[Angus Dolan]

Homework Statement

Hello, I have a homework question that I'm having difficulty with, it is:
A car travels due east (bearing 90) from point A for 6km to point B and then North-west (bearing 315) for 4.0km to point C.
By constructing a vector diagram, or otherwise, find the resultant displacement (magnitude and direction) of the car at point C from A.

Homework Equations

I don't think pythagoras theorem works here, as there is no right-angled triangle present. Although, I may be incorrect.

The Attempt at a Solution

I've drawn a vector diagram, head to tail, and measured the displacement, it comes to 4.3km at a bearing of 50. Is that correct?

 

[SaltyBriefs]

You can try other methods of finding vector C, you can find the components of vector A, and vector b

Remember finding the magnitude or resultant vector is
\vec{R} = \vec{A} + \vec{B}

which is really
\vec{R} = (A_{x} ) (B_{x} ) + (A_{y} ) (B_{y} )

A_{y} = (\vec{A}) (sin \theta)
A_{x} = (\vec{A}) (cos \theta)


B_{y} = (\vec{A}) (sin \theta)
B_{x} = (\vec{A}) (cos \theta)

The Ax, Ay, Bx, By equations are derived from this idea

 

[SaltyBriefs]

I would plug and chug for you, but I'm kind of confused by the bearings.

 

[SaltyBriefs]

Don't rely on measuring the displacement vector. Sometimes the ruler isn't as precise, also it will help you in the long run to have these equations in your tool box.

 

[SaltyBriefs]

Let me know if you solved it, or if it helped. So I can get some personal feedback, because I don't want to be misinforming people lol.