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.
1 answer:
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 °
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