Forces A and B act at a point. The sum of their magnitudes is 50 N and the magnitude of their resultant is 20 N. If the resultant is at 90^ with the smaller force, the magnitudes of A and B, in N are

Step-by-step solution

Let the magnitudes of the two forces be F₁ and F₂ with F₁ Given that the sum of their magnitudes is 50 N : F₁ + F₂ = 50 The resultant R is perpendicular to the smaller force F₁ . The angle made by the resultant with F₁ is given by: = F₂ F₁ + F₂ Since = 90^ , the denominator must be zero: F₁ + F₂ = 0 = - F₁ F₂ The magnitude of the resultant is given by: R^2 = F₁^2 + F₂^2 + 2F₁ F₂ Substituting = - F₁ F₂ and R = 20 N : 20^2 = F₁^2 + F₂^2 + 2F₁ F₂ (- F₁ F₂ ) 400 = F₁^2 + F₂^2 - 2F₁^2 F₂^2 - F₁^2 = 400 (F₂ - F₁)(F₂ + F₁