Question

What is the magnitude and direction of the resultant force?

A. Magnitude: 25 N, direction: 45 degrees above F1
B. Magnitude: 50 N, direction: 45 degrees above F1
C. Magnitude: 75 N, direction: 45 degrees below F1
D. Magnitude: 75 N, direction: 45 degrees above F1

Answer 1

The magnitude of the resultant force is 75 N, and its direction is 45 degrees above F1. Option D is the correct answer.

Step-by-step explanation:

Vector Addition:

The resultant force (R) is obtained by vector addition of forces F1 and F2 using the parallelogram law.

Components of Forces:

Breaking down forces F1 and F2 into their horizontal (F_{1x}, F_{2x}) and vertical (F_{1y}, F_{2y}) components.

Resultant Components:

Adding the horizontal and vertical components separately to find the resultant components (R_x, R_y).

Resultant Magnitude and Direction:

Calculating the magnitude (R) and direction (θ) of the resultant force using R = sqrt(R_x^2 + R_y^2) and θ = arctan(R_y/R_x).

Final Answer:

The calculated magnitude is 75 N, and the direction is 45 degrees above F1, matching option D.