How to Add Displacement Vectors Using the Component Method

[elleleeanne]

Homework Statement

Use the component method to add the following displacement vectors.
D1= 25 m [N 30 W], D2= 30 m [N 40 E], D3= 35 m [S 25 W]

Homework Equations

I know all of the equations for vx, vy and the five equations. I also know sin, cos, tan and velocity, displacement equations.

The Attempt at a Solution

My attempt was to solve d1 and d2 displacement, than solve d2 and d3 displacement. Using those to displacements solve for the whole graph. Did not end up working for me. I need help, please and thank you!

 

[omoplata]

Take the component of each vector to the North, then add them together. That is the component to the North of your final resultant vector. Then take the component of each vector to the West, then add them together. That is the component to the West of your final resultant vector.

 

[elleleeanne]

Take the component of each vector to the North, then add them together. That is the component to the North of your final resultant vector. Then take the component of each vector to the West, then add them together. That is the component to the West of your final resultant vector.

I did that and I got the wrong answer?

 

[omoplata]

Post what you did here. Let's see where you went wrong.

 

[elleleeanne]

Post what you did here. Let's see where you went wrong.

D1 & D2
dx=25cos30 = 21.65 w+22.98 E = 1.33 E dy=26sin30+30sin40= 12.5 N+19.28 N = 31.78 N

c^2=a^2+b^2 C=31.8 m
tan= 1.33/31.78 =2.41 therefore, 31.8 m [N 2.4 E]

D1 & D3
dx=25cos60W+35cos65W =27.3 W Dy=25sin60N+35sin65=10.07 S

C²=27.3²+10.07²= 29.1 m
Tan= 27.3/10.07 =69.75 therefore, 29.1 m [W 69.75 S]

Then it just seems to go downhill from there...

 

[omoplata]

Does [N 30 W] mean 30 degrees to the West from North, or does it mean 30 degrees to the North from West?

I thought it meant 30 degrees to the West from North.

I see that you've tried to find the resultant vectors of pairs D1&D2 and then D1&D3.

It'll be easier if you add the components of D1, D2 and D3, all at once.

Otherwise, if you find the resultant the D1&D2, then you have to add the components of that resultant vector with D3 to get the final resultant vector.

 

[elleleeanne]

Does [N 30 W] mean 30 degrees to the West from North, or does it mean 30 degrees to the North from West?

I thought it meant 30 degrees to the West from North.

I see that you've tried to find the resultant vectors of pairs D1&D2 and then D1&D3.

It'll be easier if you add the components of D1, D2 and D3, all at once.

Otherwise, if you find the resultant the D1&D2, then you have to add the components of that resultant vector with D3 to get the final resultant vector.

How would you add all the vectors together at once? just using the dx method? so
dx=25cos30E+30cos40W+35cos65E
and dy=25sin20N+30sin40N+35sin65S

But then how would you use the c²=a²+b²?

 

[omoplata]

Yeah, that's the idea. Add all the East and West components together and get one value for dx. Add all the North and South components together and get one value for dy.

Then $c^2 = dx^2 + dy^2$.

I still don't know what [N 30 W] means. Without knowing that I can't check wheter your answers are correct or not.

 

[elleleeanne]

Yeah, that's the idea. Add all the East and West components together and get one value for dx. Add all the North and South components together and get one value for dy.

Then $c^2 = dx^2 + dy^2$.

I still don't know what [N 30 W] means. Without knowing that I can't check wheter your answers are correct or not.

I solved it and got a completely wrong answer. the N 30 W means angle 30 is closer to the north direction.

 

[omoplata]

the N 30 W means angle 30 is closer to the north direction.

In that case you've resolved it to components the wrong way. Check your "sin"s and "cos"s.

Look at "Resolution into components" in http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html" page.