The greatest and smallest resultant of two forces acting at a point is 10 N and 6 N respectively. If each force is increased by 3 N, find the magnitude of the new resultant forces when acting at a point while being perpendicular to each other:

Explanation

To solve the problem, recognize that the greatest resultant (10 N) and smallest resultant (6 N) of two forces F1 and F2 are given by the formulas: F1 + F2 = 10 and |F1 - F2| = 6. Solving these equations gives F1 = 8 N and F2 = 2 N. When each force is increased by 3 N, the new forces become F1 = 11 N and F2 = 5 N. Since the forces are perpendicular, use the formula for the resultant of perpendicular vectors: R = √(F1² + F2²) = √(11² + 5²) = √(121 + 25) = √146 ≈ 12.1 N. Thus, the correct answer is 12.1 N. The other options do not correctly apply this calculation method.