Find the magnitude and direction of the resultant of two forces of 250 pounds and 45 pounds at angles of 25 degrees and 250 degrees with the x-axis, respectively.

Answer 1

This is a standard vector addition problem.

Add the x and y components of the two vectors separately. The x component sum is
Fx = 250 cos 25 + 250 cos 250) = 226.6 -85.5 = 137.1

The y component sum is
Fy = 250 sin 25 + 250 sin 250 = -129.3
Use the Pythagorean theorem for the magnitude of the resultant. Its direction in quadrant IV. Use the
tan^-1 Fy/Fx for the direction