Two forces with magnitudes of 100 and 50 pounds act on an object at angles of 50° 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.
Forces in direction x: fx1 = 100 * cos (50) = 64.28 fx2 = 50 * cos (160) = - 46.99 The resultant is: fx = fx1 + fx2 = 17.29
Forces in direction y: fy1 = 100 * sine (50) = 76.60 fy2 = 50 * sine (160) = 17.10 The resultant is: fy = fy1 + fy2 = 93.70 The magnitude of the resulting force is: f = root (fx ^ 2 + fy ^ 2) f = root ((17.29) ^ 2 + (93.70) ^ 2) f = 95.28 The angle is: theta = atan (fy / fx) theta = atan (93.70 / 17.29) theta = 79.55 degrees Answer: The direction and magnitude of the resultant force are: f = 95.28 pounds at theta = 79.55 degrees
