# Find the magnitude of the resultant force and the angle it makes with the positive x-axis.

Asked by wiki @ in Mathematics viewed by 115 People

Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 28 lb and b = 12 lb. Round your answers to one decimal place.)

a = 45 degree positive on x & y axis.
b = 30 degree below x-axis. I guess negative on y & x.

Magnitude of R = 16.7 lb

Angle = 55.7°

Step-by-step explanation:

Given:

a = 28 lb

b = 12 lb

a = 45 degree positive on x & y axis.

b = 30 degree below x-axis. negative on y & x.

Resolving the two forces to vector form, we have

a = (28cos45)i + (28sin45)j

b = (-12cos30)i + (-12sin30)j

The resultant force vector R = a +b

R = (28cos45 - 12cos30)i + (28sin45 - 12sin30)j

R = 9.41i + 13.80j

Magnitude of R = √(9.41^2 + 13.80^2) = 16.7 lb

Angle = taninverse (13.80/9.41) = 55.7°

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