Question

Two forces with magnitudes of 90 and 50 pounds act on an object at angles of 30° and 160°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

Force 1, F1 = 90, angle 30°

Force 2, F2 = 50, angle 160°

F1 = 90 cos(30) i + 90 sin (30) j
F2 = 50 cos (160) i + 50 sin (160) j

F1 = 90*0.866 i + 90*0.5 j
F2 = 50*(- 0.940) i + 50*0.342 j

F1 = 77.94 i + 45 j
F2 = -47 i +17.10 j

Resultant force, Fr = F1 + F2

Fr = [77.94 - 47.00] i +[45 +17.10]j = 30.94 i + 62.10 j

Magnitude = √[30.94 ^2 + 62.10^2] = 69.38 pounds

Direction  = arctan[62.10/30.94] = 63.52 °