Question

The three displacement vectors in the drawing have magnitudes of A = 4.60 m, B = 4.85 m, and C = 3.70 m. Find the resultant (magnitude and directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above or below the positive or negative x axis. (Assume α = 25° and β = 58°. Give an answer between 0 and 90°.)

Answer 1

here

given

a = 4.6 m

theta1 = 180-25 = 155 degrees

ax = acos155 = 4.6cos155 = -4.17 m

ay = asin155 = 1.94 m

b = 4.85 m

tehta2 = 58 degrees

bx = 4.85cos58 = 2.57 m

by = 4.85sin58 = 4.11 m

c = 3.7 m

theta3 = 270 degrees

cx = 3.7 cos270 = 0

cy = 3.7sin270 = -3.7 m

x component of resusltant vector = rx = ax+bx+cx

rx = -1.6 m

y component of resusltant vector

ry = ay+by+cy

ry = 2.35 m

magnitude = r = sqrt(rx^2+ry^2) = 2.84 m

direction = tan^-1(2.35/-1.6) = 55.75 above the negative x axis