What are the steps for solving this problem? Copy of Vector A has a magnitude of

Question

What are the steps for solving this problem?

Copy of Vector A has a magnitude of 8 and is at an angle of 33.7 degrees measured counter-clockwise from the x axis. Vector B has a magnitude of 12 and is at an angle of 103.6 degrees measured counter-clockwise from the x axis. Vector C has a magnitude of 16 and is at an angle of 180 degrees measured counter-clockwise from the x axis. Lastly, Vector D has a magnitude of 17 and is at an angle of 289.3 degrees measured counter-clockwise from the x axis. If R = A + B + C - D, find the magnitude of R.

Explanation / Answer

given,

A = 8 units at 337 degrees

B = 12 units at 103.6 degrees

C = 16 units at 180 degrees

D = 17 units at 289.3 degrees

R = A + B + C - D

x component of R = x component of (A + B + C - D)

x component of R = 8 * cos(33.7) + 12 * cos(103.6) + 16 * cos(180) - 17 * cos(289.3)

x component of R = -17.78 units

y component of R = y component of (A + B + C - D)

y component of R = 8 * sin(33.7) + 12 * sin(103.6) + 16 * sin(180) - 17 * sin(289.3)

y component of R = 32.147 units

magnitude of R = sqrt(17.78^2 + 32.147^2)

magnitude of R = 36.736

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