Final answer:
The magnitude of the resultant force when a 109 N force and a 49 N force act at a 90-degree angle to each other is calculated using the Pythagorean theorem, resulting in approximately 119.5 N.
Step-by-step explanation:
To find the magnitude of the resultant force when a 109 N force and a 49 N force act on the same object at 90 degrees to each other, we can use the Pythagorean theorem. The forces act perpendicularly, so we can treat them as vector components of the resultant force. Therefore, the magnitude of the resultant force (R) can be calculated using the following formula:
R = √(F1² + F2²)
Substituting the given forces into the formula:
R = √(109 N² + 49 N²) = √(11881 N² + 2401 N²) = √14282 N²
R ≈ 119.5 N
Thus, the magnitude of the resultant force is approximately 119.5 N.