Question

two forces of 19.8 pounds and 36.5 pounds act on a body with an angle of 61.4 degrees between them. on a coordinate plane, a vector on the x-axis is labeled 19.8 pounds. a vector labeled 36.5 pounds forms angle 61.4 degrees with the x-axis. choose the correct approximation for the magnitude of the resultant vector. 45.5 pounds 21.3 pounds 49.2 pounds 2416.2 pounds

Answer 1

The magnitude of the resultant vector is approximately 49.2 pounds, calculated using the law of cosines for vector addition.

Step-by-step explanation:

To find the magnitude of the resultant vector of two forces acting at an angle, we can use vector addition methods. In this case, since the vectors are not perpendicular, we will have to use the law of cosines to find the resultant:
FR = √(F12 + F22 + 2 × F1 × F2 × cos(θ))

Let's plug in the values:
FR = √(19.82 + 36.52 + 2 × 19.8 × 36.5 × cos(61.4°))

Calculate the cosine of the angle and multiply by the forces, then add the squares of the individual forces and take the square root:
FR ≈ √(19.82 + 36.52 + 2 × 19.8 × 36.5 × 0.4848)

FR ≈ √(392.04 + 1332.25 + 696.1968)

FR ≈ √(2420.4868) ≈ 49.2 pounds