Question

Four horizontal forces of magnitudes 1 N, 2 N, 3N, and 4N act at a point in the direction whose bearings are 000⁰, 060⁰, 120 ⁰, and 270 ⁰ respectively and a 5th horizontal force of magnitude 3 N now acts at the same points so that the resultant of all five forces has a bearing of 090⁰. Find the bearing of the 5th force.)

Answer 1

To find the bearing of the 5th force, we need to consider the resultant of all five forces. We can use vector addition to find the magnitude and direction of the resultant force. Once we have the resultant force, we can find the magnitude of the 5th force and its bearing.

Step-by-step explanation:

To find the bearing of the 5th force, we need to consider the resultant of all five forces. The given forces have bearings of 000⁰, 060⁰, 120 ⁰, and 270 ⁰ respectively. The resultant force has a bearing of 090⁰. Since the magnitudes of the forces are given and the bearings are known, we can use vector addition to find the magnitude and direction of the resultant force. Once we have the resultant force, we can subtract the magnitudes of the previous four forces from it to find the magnitude of the 5th force. Finally, using the given bearing of 090⁰ for the resultant force, we can determine the bearing of the 5th force.