Vector Addition Help: Find Resultant of 5 Vectors

[katieb123]

Homework Statement

Find the resultant for the following directions.
20 degrees east of south for 1/2"
80 degrees South of west for 5"
15 degrees west of north for 1"
35 degrees North of East for 3"
40 degrees South of East for 1"

Homework Equations

R2 = a2 + b2

The Attempt at a Solution

i graphed the measurements with each 5" = 1/2" on graph paper. then i connected the tail of the first vector to the head of the end point and measured the resultant but when i calculated it i got 31.55, to calculate this i found the x,y for each vector. vector 1- 4.69,-1.71. vector 2- - and -8.68, -49.24. vector 3- -9.66, 2.59. vector 4- 24.57, 17.21, vector 5- 8.19, -5.74. i added up the totals for each x and y then used the resultant formula to get the resultant to be 31.55. is that correct?

 

[gneill]

Show your calculations!

 

[katieb123]

i showed calculations can you help?

 

[gneill]

i graphed the measurements with each 5" = 1/2" on graph paper. then i connected the tail of the first vector to the head of the end point and measured the resultant but when i calculated it i got 31.55,

31.55 was a value you measured on the graph paper, or was it a numerical calculation? Perhaps I'm not clear on what the point of the exercise is. Is the idea to find the resultant by graphical method or by numerical calculation? Or both?

to calculate this i found the x,y for each vector. vector 1- 4.69,-1.71. vector 2- - and -8.68, -49.24. vector 3- -9.66, 2.59. vector 4- 24.57, 17.21, vector 5- 8.19, -5.74. i added up the totals for each x and y then used the resultant formula to get the resultant to be 31.55. is that correct?

Can you pick a vector, say vector 1, and show how you found the x and y components?

 

[katieb123]

31.55 was found by calculations. i was asked to find both ways graphically and by calculator.

 

[katieb123]

i found the vectors x, y by plugging it in my calculator in an app

 

[gneill]

31.55 was found by calculations. i was asked to find both ways graphically and by calculator.

i found the vectors x, y by plugging it in my calculator in an app

Okay. I think your calculator app is giving you the x & y components in reverse order (or you're swapping them somehow), and they seem to be multiplied by 10.

If we take a Cartesian coordinate system where y is North and x is East, then for the first vector the angle is 20° East of South, which is -90° + 20° = -70°. The components are

x = (1/2)*cos(-70°) ; y = (1/2)*sin(-70°)

x = 0.1710 ; y = -0.4698

You should verify that your app gives you these results for the components of vector 1. After that, construct a table with the magnitude, angle, and components for each vector.