Final answer:
The magnitude of the normal force acting on Freida, who has a mass of 65 kg and is standing on a hill with a 12-degree slope, is approximately 637 N.
Step-by-step explanation:
To find the magnitude of the normal force acting on Freida as she stands on a hill with a 12-degree slope, we must consider the component of her weight that acts perpendicular to the surface of the slope. This is because the normal force is always perpendicular to the surface the object is in contact with. We can calculate the normal force (N) using the formula N = mg cos(\theta), where m is the mass, g is the acceleration due to gravity (9.80 m/s²), and \theta is the slope angle in radians.
Using Freida's mass (65 kg) and the given value of g (9.80 m/s²), we can calculate:
N = 65 kg × 9.80 m/s² × cos(12 degrees)
Converting 12 degrees to radians: 12 degrees × (\pi/180) = 0.209 radians
Hence:
N = 65 × 9.80 × cos(0.209)
After the calculation, we find that N is approximately 637 N, which is closest to option B.