Two forces, 364 N at 19° and 253 N at 32° are applied to a car in an effort to accelerate it. The resultant forces of these two forces is 558.72 N. What is the direction of the resultant force (in relation to forward, with counterclockwise considered positive, with -180°

Question

Two forces, 364 N at 19° and 253 N at 32° are applied to a car in an effort to accelerate it. The resultant forces of these two forces is 558.72 N. What is the direction of the resultant force (in relation to forward, with counterclockwise considered positive, with -180° < theta < +180. Answer in units of degrees.

bobpursley · Answer

What in the world is the direction in relation to forward?

The angle between the two forces is 13 degrees (tail to tail). So if you add them head to tail, the angle between them is 180-13. draw the triangle. Use the law of sines to find the angle of the resultant with respect to the triangle.

558.72/sin(167)=364/sinAlpha

SinAlpha= sin167*364/558.72=
alpha=8.4 degrees

or Theta= 32-8.4 =23.6 deg