Question

two forces act on a body so the resultant is a force of 68.3 pounds. the angles between the resultant and the forces measure 46 degrees and 38 degrees. the applied forces have different magnitudes. what is the larger magnitude of these forces? 49.4 pounds 52.7 pounds 41.5 pounds 53.6 pounds

Answer 1

The larger magnitude of the forces is 52.7 pounds.

Step-by-step explanation:

To find the larger magnitude of the forces, we use the concept of vector addition. The given resultant force of 68.3 pounds is the vector sum of two forces acting at different angles. Using the law of cosines, we can calculate the magnitude of the resultant force. Then, by considering the given angles, we can determine the individual magnitudes of the forces.

The law of cosines states that for any triangle, the square of the length of one side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle. Applying this to the forces, we find the magnitude of each force by rearranging the formula and solving for the unknown magnitudes.

Given the angles of 46 degrees and 38 degrees, the larger magnitude of the forces corresponds to the larger angle. By plugging in the known values and solving for the larger force, we find that it is 52.7 pounds.

In summary, the larger magnitude of the forces acting on the body is determined by considering the angles and using the law of cosines to calculate the individual force magnitudes.