# Magnitude of displacement

1. Dec 11, 2011

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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°

2. Dec 11, 2011

### Staff: Mentor

Your breakdown of Vector C isn't quite right.

3. Dec 11, 2011

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

4. Dec 11, 2011

### Staff: Mentor

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.

5. Dec 11, 2011

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.

6. Dec 11, 2011

### Staff: Mentor

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.

7. Dec 11, 2011