This problem is intended for you to review vector addition and for me to make su

Question

This problem is intended for you to review vector addition and for me to make sure you can actually do this. So, impress me Write this problem in full detail, show off how well you understand vector components, unit-vector notation, directions reported with angles, calculating a resultant, and keeping track of units and significant digits. Write it as if intended to be published in a Solutions Manual. Find the resultant of these two vectors, using the component method, as described in pages 14 to 19 from the textbook. Report the resultant in two different ways: (a) In unit-vector-notation (physics notation with i^, j^, k^, as shown in page 19, eq. 1.15.) (b) As a magnitude and unique direction (report the direction as a positive angle, between 0 degree and 360 degree, measured counter-clockwise starting from the +x axis.) Use extra pages if needed to truly show off how nicely you can do this.

Explanation / Answer

angle between two vectors is = 32+90+24 = 146 degrees

f1 = 4.5 N

f2 = 5.5 N

f1x = f1cos(360-24) = 4.11 N

f1y = 4.5sin(360-24) = -1.83 N

f2x = f2cos(90+32) = -2.91 N

f2y = 5.5sin(90+32) = 4.66 N

fx = f1x+f2x = 1.2 N

fy = f1y+f2y = 2.83 N

f = sqrt(fx^2+fy^2) = 3.07 N

theta = tan^-1(fy/fx) = 67.02 degrees from x axis

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