46.  The three displacement vectors in the drawing have magnitudes of A = 5.00 m, B = 5.00 m, and C = 4.00 m. Find the resultant (magnitude and directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis.

 

 

So let’s first find the x and y components of the three vectors:

 

Note: minus sign due to fact is clearly pointing in negative x direction.

Note: this is pointing in positive y direction, so it is positive

 

 

 

 

Now find the net x component by adding up individual x-components and do the same with the y components to find net y-component.

 

 

 

Now that we have just an x-component and a y-component we can use Pythagorean therim.

 

 

We find the angle relative to negative x axis since the net resultant x-component is negative

 

Final Answer for Resultant is

 

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This page last updated on January 11, 2020