# Vector Addition Help: Find Resultant of 5 Vectors

• katieb123
Use the same sign conventions for angles as I did for vector 1.In summary, the problem asks for the resultant of five vectors with given directions and magnitudes of 1/2", 5", 1", 3", and 1". The first vector is 20 degrees east of south, the second is 80 degrees south of west, the third is 15 degrees west of north, the fourth is 35 degrees north of east, and the fifth is 40 degrees south of east. The resultant of these vectors was calculated using both graphical and numerical methods, with the final result being 31.55. However, there may be discrepancies in the calculations due to incorrect x and y components being used.

## 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"

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?

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i showed calculations can you help?

katieb123 said:
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?

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

katieb123 said:
31.55 was found by calculations. i was asked to find both ways graphically and by calculator.

katieb123 said:
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.