# Vector addition. finding x & y components, the magnitude, & the angle

## Homework Statement

Two vectors have equal magnitude of 14.8 m and the angles are theta 1 = 32 deg & theta 2 = 108 deg. Find a) their x component b)their y component of vector sum $$\vec{}r$$ c) the magnitude of $$\vec{}r$$ & d) the angle $$\vec{}r$$ makes with the positive direction of the x axis.

## Homework Equations

Ax = Acos(theta)
Ay = Asin(theta)
Rx = Ax + Bx
Ry = Ay + By
R = sqrt of [Rx (squared) + Ry (squared)]
theta = arctan of (Ry/Rx)

## The Attempt at a Solution

a) First, I found Ax by doing 14.8 * cos32 which gave me 12.55
then i found Bx by multiplying 14.8*cos108 which gave me -4.57
I added those two for Rx] & got 7.98 m

b) i found the y of A by doing 14.8sin32 = 7.8428. i found the y of B by doing 14.8sin108 = 14.0756. i added 7.8 & 14.0756 to get Ry & got 21.9 m

c) i took the square root of (7.98(squared) + 21.9(squared) & got 23.3 m

d) to find theta i took the inverse tangent of 21.9/7.98 & got 7.9776 degrees

the problem is that all of my answers are wrong & i'm not sure where my issue is. any help would be much appreciated. thank you

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vela
Staff Emeritus
Homework Helper
Your answers look fine to me except for the angle r makes with the x-axis. Your approach is fine, so you probably just plugged it into the calculator incorrectly.

thanks. i figured it out. i needed to use 140 for theta 2 (108+32). because B's angle was 108 plus the 32