Find the Magnitude and Direction of a Force Vector

What is the magnitude and direction of a force vector with components Fx = -5 lbs and Fy = 10 lbs?

The magnitude of the force vector can be calculated using the Pythagorean theorem, which results in approximately 11.2 lbs. The direction of the force vector can be determined using trigonometry and is approximately 116.57° counterclockwise from the positive x-axis.

Magnitude of the Force Vector

The magnitude (F) of a force vector with components Fx = -5 lbs and Fy = 10 lbs can be calculated using the formula: F = √(Fx² + Fy²). Substitute the values of Fx and Fy into the equation: F = √((-5 lbs)² + (10 lbs)²) ≈ √(25 + 100) ≈ √125 ≈ 11.2 lbs.

Direction of the Force Vector

To determine the direction of the force vector, we use the formula: θ = arctan(Fy / Fx). Substitute the values of Fy and Fx into the equation: θ = arctan(10 lbs / -5 lbs) ≈ arctan(-2) ≈ -63.43°. However, this angle is measured clockwise from the positive x-axis. To convert it to counterclockwise direction, we add 180°: θ = -63.43° + 180° ≈ 116.57°. Therefore, the magnitude of the force vector is approximately 11.2 lbs, and its direction is approximately 116.57° counterclockwise from the positive x-axis.
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