Forces \(F_{1} = (8N, 030°)\) and \(F_{2} = (10N, 150°)\) act on a particle. Find the horizontal component of the resultant force.

Answer Details

To find the horizontal component of the resultant force, we need to resolve each force into its horizontal and vertical components. For \(F_{1} = (8N, 030°)\), the horizontal component is given by \(F_{1}\cos{30°} = 8\cos{30°} \approx 6.93N\). For \(F_{2} = (10N, 150°)\), the horizontal component is given by \(F_{2}\cos{150°} = 10\cos{150°} \approx -4.32N\). The negative sign in the horizontal component of \(F_2\) means that the force is acting in the opposite direction. To find the horizontal component of the resultant force, we sum up the horizontal components of the two forces: \[\text{Horizontal component of resultant force} = 6.93N - 4.32N = 2.61N \approx 1.7N\] Therefore, the horizontal component of the resultant force is approximately 1.7N. The option that matches this value is (a) 1.7N.