A 55 kg skier rests on a hill that has an angle of 25° to the horizontal. What is the magnitude of the normal force the hill exerts on the skier?

M g cos 25

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To find the magnitude of the normal force exerted by the hill on the skier, we need to resolve the weight of the skier into its vertical and horizontal components.

First, we need to find the vertical component of the weight. We can calculate this using the formula:

Vertical Component = Weight * cos(angle)

Weight = mass * acceleration due to gravity (g)

Using the given mass of the skier (55 kg) and the acceleration due to gravity (9.8 m/s^2):

Weight = 55 kg * 9.8 m/s^2 = 539 N

Now, let's calculate the vertical component:

Vertical Component = 539 N * cos(25°)

Next, we need to calculate the horizontal component of the weight using the formula:

Horizontal Component = Weight * sin(angle)

Using the given weight (539 N) and the angle (25°):

Horizontal Component = 539 N * sin(25°)

Now, the magnitude of the normal force is equal to the vertical component of the weight because the normal force balances the weight in the vertical direction. So, the magnitude of the normal force is:

Magnitude of Normal Force = Vertical Component

Finally, you can substitute the value of the vertical component into the equation to find the magnitude of the normal force.