Finding magnitude and direction

[emsfavis]

Homework Statement

The resultant vector of the four displacement vector A B C D is 1000m, with direction 60° N of W. The three vectors A B C are:
A=200m,S
B=300m,45° S of W
C=400m,30° E of N

a.) Find the magnitude of the fourth vector
b.) find the direction of the fourth vector

Homework Equations

m = meter

The Attempt at a Solution

can i get a help using component method

what i did was get the x and y coordinate for the 3 vectors first,

1st vector = 200 m south

x-coordinate = 0
y-coordinate = -200
End point of 1st vector = (0, -200)

2nd vector = 300 m in a direction 45° south of west

x-coordinate = 300 * sin 45° west= -300 * sin 45° = -212.1 West
y-coordinate = 300 * cos 45 south = -300 * cos 45°= -212.1 South

3rd vector = 400 m at 30° east of north.

x-coordinate = 400 * sin 30° east = +400 * sin 30° = 200 East
y-coordinate = 400 * cos 30° north = +400 * cos 30° = 346.4 North

*THEN WHAT SHOULD I DO NEXT? and also am i doing the right thing?

 

[NascentOxygen]

C=400m,30° E of W

typo

Your method is correct.

The unknown vector has a horizontal component=
horiz comp of the sum - sum of other 3 vectors' horiz components

Same for the vertical component

 

[RTW69]

You are definitely on the right track. Use the same procedure to find the x and Y components of the resultant vector. Remember that the resultant vector is the sum of vectors, A,B,C and D.

I would make a table of the x and y components of vectors A,B,C. The sum of these vectors when added to the x and y components of vector D must equal the x and y components of the resultant vector.

 

[emsfavis]

typo

Your method is correct.

The unknown vector has a horizontal component=
horiz comp of the sum - sum of other 3 vectors' horiz components

Same for the vertical component

my mistake thanks for the info, i'll post my computations of that when i get home from school later :D thanks

You are definitely on the right track. Use the same procedure to find the x and Y components of the resultant vector. Remember that the resultant vector is the sum of vectors, A,B,C and D.

I would make a table of the x and y components of vectors A,B,C. The sum of these vectors when added to the x and y components of vector D must equal the x and y components of the resultant vector.

ok sir, ill do that, ill post it later. thanks :D

 

[emsfavis]

Just want to ask if I'm doing the right thing to find vector D and what should be the direction?

*Sum of x and y coordinate

Sum of X = 0 + (-212.1) + 200 = -12.1 West

Sum of Y = -200 + (-212.1) + 346.4 = -65.7 South

*Magnitude of vector D

Magnitude of vector D = Square root of ((-12.1)^2 + (-65.7)^2) = 66.80 m

 

[emsfavis]

^ is that the magnitude and direction already? or is it not right? and i still have to do something?

 

[emsfavis]

^^ ... ok my mistake on the last 2 posts. hmm.. I am really having trouble trying to get D. can someone help me

 

[NascentOxygen]

Just want to ask if I'm doing the right thing to find vector D and what should be the direction?

*Sum of x and y coordinate

Sum of X = 0 + (-212.1) + 200 = -12.1 West

Sum of Y = -200 + (-212.1) + 346.4 = -65.7 South

*Magnitude of vector D

Magnitude of vector D = Square root of ((-12.1)^2 + (-65.7)^2) = 66.80 m

Right so far.

Sometimes it's easier to think in terms of addition, rather than subtraction. So write:

Horiz components of 3 vectors + horiz comp of 4th = horiz comp of total

Same for the vertical components.

In addition, you can neatly sketch the vector diagram, using a ruler and protractor. Draw in the 3 vectors you are given, one at a time, graphically adding them as you go. Draw in the vector you are told is their sum. And you can pictorially see in front of you what extra vector must be drawn in so that the summation of the individual four vectors joins up to become equal to a vector ending at 1000 at 60 deg W of N.

Don't sit staring at numbers; sketch what you know. Your sketch will guide you on how to express that fourth vector. This whole question can (and should) be done on a set of x-y co-ordinates.