# 2D Motion Finding the resultant using components

1. Nov 27, 2011

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

A person walks 20m [N20(degrees)E], then 120m [N50(degrees)W], then 150m[W], and finally 30m [S75(degrees)E]. Find the person's final displacement.

2. Relevant equations

Is my solution correct? The textbook answers are 230m[N23(degrees)W]
What did I do incorrect? Explain please :/ :(

3. The attempt at a solution

*Horizontal Component*
(20m)cos70
-(120m)cos40
-150m
(30m)cos75

Total for horizontal component: -227m

*Vertical Component*
(20m)sin70
(120m)sin40
0
-(30m)sin75

Total for vertical component: 67m

Total displacement = sqrt(-227m^2)+(67m^2)
=237m

Direction: tan^-1(67m/227m)
=16.4

2. Nov 27, 2011

c'mon someone must be here

D:

3. Nov 27, 2011

### physicsvalk

When you say "[N20(degrees)E]" do you mean 20 degrees North of East?

4. Nov 27, 2011

yes

it basically says [N20E]

Expect the 20 has a degree subscript. I suck with reading degree's

5. Nov 27, 2011

### physicsvalk

It seems like you're first finding the compliment of the angle before you're breaking down the vector. If you do this, note that you're looking at the opposite angle and then the sine/cosine convention would change.

EDIT:
Try solving the problem by leaving the angles (instead of finding the compliment - which would just make things harder) they way they are and drawing out triangles to represent displacements in the x- and y-direction. Then, after you break down all of them, sum each x- and y- and take the vector sum.

Last edited: Nov 27, 2011
6. Nov 27, 2011