Question

If a force of magnitude 118 is directed 45 degrees south of the east, what are its components? What is the force of components Fx=? and Fy=?

Answer 1

The components of a force of 118 N directed 45 degrees south of the east are 83.45 N eastward (Fx) and -83.45 N southward (Fy), both rounded to two decimal places.

Step-by-step explanation:

If a force of magnitude 118 N is directed 45 degrees south of the east, its components can be found using trigonometric functions. To solve for the components, we'll use the cosine function for the x-component (East-West axis) and the sine function for the y-component (North-South axis). Since the force is directed south of east, the x-component will be positive (eastward) and the y-component will be negative (southward).

The x-component (Fx) is Fx = 118 N × cos(45°) and the y-component (Fy) is Fy = -118 N × sin(45°). Plugging in the values, we get:

• Fx = 118 N × 0.707 ≈ 83.45 N (Eastward)
• Fy = -118 N × 0.707 ≈ -83.45 N (Southward)

Thus, the components of the force are approximately 83.45 N in the eastward direction and -83.45 N in the southward direction.