To calculate the resultant force and direction, we can use the parallelogram law of vectors. Draw a diagram showing the two forces and their directions.
Draw a parallelogram with the two forces as adjacent sides. The resultant force (R) is the diagonal of the parallelogram.
Use the cosine formula to calculate the magnitude of R:
R = √(6^2 + 8^2 - 2(6)(8)cos(50°))
Simplify and solve for R.
R ≈ 10.6 N
Use the arctangent function to find the direction of R:
θ = arctan(8/6) = 30.9° north of west
So the resultant force is approximately 10.6 N, directed 30.9° north of west. This is the force that will cause the body to move in a particular direction.
