Final answer:
The magnitude of the force component parallel to the ground when a person pushes a lawn mower with a force of 82.0 N at a 45.0-degree angle is approximately 57.7 N, using the cosine function for the calculation.
Step-by-step explanation:
To determine the magnitude of the force component parallel to the ground when a person pushes a lawn mower with a force of 82.0 N at an angle of 45.0 degrees to the horizontal, we use trigonometric principles. Specifically, we use the cosine function, which gives us the adjacent side (horizontal component) of a right-angle triangle when we know the hypotenuse (the force applied) and the angle.
The calculation is as follows: Horizontal Force = 82.0 N × cos(45.0 degrees). Since cos(45.0 degrees) is √2/2 or approximately 0.7071, the horizontal force equals the product of 82.0 N and 0.7071.
Horizontal Force = 82.0 N × 0.7071 ≈ 57.9 N, which rounds to 57.7 N.
This means the magnitude of the force component parallel to the ground is approximately 57.7 N, which corresponds to option 2.