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Find the resultant force
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5 stepsIdentify the given forces and the angle between them.
We have two forces: units (acting horizontally) and units.
The force is at an angle of from the North axis. Since the North axis is perpendicular to the horizontal force , the angle between and is .
Let be the angle between the two forces, so .Calculate the magnitude of the resultant force using the Law of Cosines.
The formula for the magnitude of the resultant of two vectors and with an angle between them is:
Substitute the values and calculate .
The magnitude of the resultant force is .
Calculate the direction of the resultant force using the Law of Sines.
The angle is the angle between the resultant force and the horizontal force units. Consider the triangle formed by , (shifted), and . The angle opposite in this triangle is . The angle is opposite the force units.
Using the Law of Sines:Calculate the value of .
The direction of the resultant force is .
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