Question

The magnitudes of the four displacement vectors shown in the drawing are A = 16.0 m, B = 11.0 m, C = 12.0 m, and D = 28.0 m. Determine the magnitude and directional angle for the resultant that occurs when these vectors are added together. 

Answer 1

for the net x component

x = 28 * cos(50) - 16 * cos(20) - 12 * cos(35)

x = -6.87 m

for the y component

y = 16 * sin(20) + 11 - 12 * sin(35) - 28 * sin(50)

y = -11.9 m

for the net displacement

magnitude = sqrt(6.87^2 + 11.9^2) = 13.74 m

magnitude of displacement is 13.74 m

as the net displacement is in third quardart

direction of net displacement = 180 + arctan(11.9/6.87)

direction of net displacement = 240 degree

the direction of net displacement is 240 degree with x axis