Question

Three men were trying to pull a tree stump out of the ground. The first man was pulling with a force of 100 N to the North. The second man was pulling with a force of 75 N at an angle of 45 degrees. The third man was pulling at 75 N at an angle of 135 degrees. What resultant force is being applied to the tree stump?

Answer 1

To find the resultant force applied to the tree stump, we need to break down each force into its x and y components. The x and y components can be found using trigonometry, and then the resultant force can be found using vector addition.

Step-by-step explanation:

To find the resultant force applied to the tree stump, we need to break down each force into its x and y components.

The first man's force of 100 N to the North has no x component but a y component of 100 N.

The second man's force of 75 N at an angle of 45 degrees can be broken down into an x component of 75 N * cos(45) and a y component of 75 N * sin(45).

The third man's force of 75 N at an angle of 135 degrees can be broken down into an x component of 75 N * cos(135) and a y component of 75 N * sin(135).

Next, we sum up the x components and the y components separately to find the resultant force in each direction. Finally, we use the Pythagorean theorem to find the magnitude of the resultant force, and use the inverse tangent function to find the angle it makes with respect to a reference direction.