THE RESULTANT OF TWO FORCES IS 50N. IF THE FORCES ARE PERPENDICULAR TO EACH OTHER AND ONE OF THEM MAKES AN ANGLE OF 30° WITH THE RESULTANT, FIND ITS MAGNITUDE

• A. 100.0N
• B. 57.7N
• C. 43.3N ✓
• D. 25.0N

The answer to the question is: C. 43.3N

To solve this problem, we can use vector addition and trigonometric functions. Let’s denote the magnitude of the first force as F1 and the magnitude of the second force as F2. Given that the resultant of the two forces is 50N, and the forces are perpendicular to each other, we can use the following equation to find the magnitude of one of the forces:

R^2 = F1^2 + F2^2

Where R is the magnitude of the resultant (50N). Since the forces are perpendicular, one force makes an angle of 30 degrees with the resultant. We can use trigonometric functions to find the magnitude of one of the forces.

Using trigonometric functions, we have:

cos(30°) = adjacent / hypotenuse

cos(30°) = F1 / 50

F1 = 50 * cos(30°)

F1 ≈ 43.3N

Therefore, the magnitude of one of the forces is approximately 43.3N.