What is the magnitude and angle of displacement given three vectors?

[laladude]

Homework Statement

Compute the magnitude of the displacement ($\vec{}R$ and the angle with respect to the x-axis.

Homework Equations

The Attempt at a Solution

A = 10m * sin30° $\hat{}y$+ 10m * cos30° $\hat{}x$

$\vec{}A$ = 5m $\hat{}y$ + 8.66m $\hat{}x$

B = 15m

C = 20m * sin80° $\hat{}x$ + 20m * cos80° $\hat{}y$

$\vec{}R$ = $\hat{}A$ + $\hat{}B$ + $\hat{}C$
$\hat{}R$ = √(43.36m)² + (1.58m)² = 64.34m

tanθ = 43.36/1.58
= 87°

Is this correct? Please help!

 

[NascentOxygen]

C = 20m * sin80° $\hat{}x$ + 20m * cos80° $\hat{}y$

Your breakdown of Vector C isn't quite right.

 

[laladude]

Your breakdown of Vector C isn't quite right.

Thanks.. Would it just be 20m * cos80° in the y-direction and none in the x-dir?

 

[NascentOxygen]

Thanks.. Would it just be 20m * cos80° in the y-direction and none in the x-dir?

No, not if that's 80 degrees to the horizontal. Unless a vector lies exactly along the x (or y) axis, it must resolve into both x and y components.

 

[laladude]

No, not if that's 80 degrees to the horizontal. Unless a vector lies exactly along the x (or y) axis, it must resolve into both x and y components.

I noticed I'm missing a negative in the y direction, but how will I correctly break it into its components? I can make a triangle from the dotted line to the bottom arrow of C, but I'm not so sure of what to use.

 

[NascentOxygen]

To make it easier to visualize, in your rough working (which only you see) draw the angle so that it's more like 70 degrees than 80 so you have more space on the paper to work with. Then construct that triangle you spoke of, and determine the lengths of its vert and horiz sides.

There is more amiss than the missing - sign.

 

[laladude]

To make it easier to visualize, in your rough working (which only you see) draw the angle so that it's more like 70 degrees than 80 so you have more space on the paper to work with. Then construct that triangle you spoke of, and determine the lengths of its vert and horiz sides.

There is more amiss than the missing - sign.

draw the triangle on the inside of the picture? I am so losttt

 

[NascentOxygen]

Vector C is almost vertical, so when you break it into its components, the longest of these components is going to be the vertical one. Check that you have this correct.