Calculating Displacement with Vectors

  • #1
Angus Dolan
1
0

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?
 
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  • #2
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
[itex]\vec{R}[/itex] = [itex]\vec{A}[/itex] + [itex]\vec{B}[/itex]

which is really
[itex]\vec{R}[/itex] = (A[itex]_{x}[/itex] ) (B[itex]_{x}[/itex] ) + (A[itex]_{y}[/itex] ) (B[itex]_{y}[/itex] )

A[itex]_{y}[/itex] = ([itex]\vec{A}[/itex]) (sin [itex]\theta[/itex])
A[itex]_{x}[/itex] = ([itex]\vec{A}[/itex]) (cos [itex]\theta[/itex])


B[itex]_{y}[/itex] = ([itex]\vec{A}[/itex]) (sin [itex]\theta[/itex])
B[itex]_{x}[/itex] = ([itex]\vec{A}[/itex]) (cos [itex]\theta[/itex])

The Ax, Ay, Bx, By equations are derived from this idea
xycomponents.gif
 
  • #3
I would plug and chug for you, but I'm kind of confused by the bearings.
 
  • #4
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.
 
  • #5
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.
 
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