2D Motion Finding the resultant using components

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SUMMARY

The discussion centers on calculating the resultant displacement of a person walking in multiple directions, specifically using vector components. The individual walked 20m [N20(degrees)E], 120m [N50(degrees)W], 150m [W], and 30m [S75(degrees)E]. The correct final displacement is 230m [N23(degrees)W], while the participant's calculation yielded 237m [W16(degrees)N], indicating a misunderstanding in angle representation and vector breakdown. Key errors involved incorrectly finding the complementary angles and misapplying sine and cosine conventions.

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Homework Statement



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.




Homework Equations



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



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


Answer= 237m[W16(degrees)N]
 
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D:
 
When you say "[N20(degrees)E]" do you mean 20 degrees North of East?
 
physicsvalk said:
When you say "[N20(degrees)E]" do you mean 20 degrees North of East?

yes

it basically says [N20E]

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

what do you mean?

My solution looks right...
I'm only off by 7m for the displacement but for the notation I got 16 degrees but it should be 23, idk how I'm off by that much.


Did you do the solution? :s
 

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