Question

Two forces of 20.0N and 50.0N act at a point and at angle of 120° to each other.

What is the magnitude of the resultant force (R)?

R = 70.0N
R = 35.0N
R = 58.1N
R = 42.4N

Answer 1

The magnitude of the resultant force when two forces of 20.0N and 50.0N act at a 120° angle to each other is calculated using the law of cosines, giving a resultant force of approximately 58.1N.

Step-by-step explanation:

We are asked to find the magnitude of the resultant force when two forces of 20.0N and 50.0N act at a point and at an angle of 120° to each other. To find the resultant force, we can use the law of cosines which is applicable for any two vectors at an angle. The formula for the magnitude of the resultant vector R is R = √(F1² + F2² + 2*F1*F2*cosθ), where F1 and F2 are the magnitudes of the two forces and θ is the angle between them.

Plugging the values into the formula, we get R = √((20.0N)² + (50.0N)² + 2*(20.0N)*(50.0N)*cos(120°)). Computing this, we find that the magnitude of the resultant force is approximately 58.1N. Therefore, the correct answer is R = 58.1N.