Final answer:
The magnitude of the net force in the vertical direction acting on the person is equal to their weight, which is 735 N. The magnitude of the normal force on the person is also 735 N. The magnitude of the net horizontal force acting on the earth due to the person cannot be determined without additional information about the coefficient of friction.
Step-by-step explanation:
1. What is the magnitude of the net force in the vertical direction acting on the person?
The magnitude of the net force in the vertical direction acting on the person is equal to their weight. The weight of the person can be calculated using the equation: weight = mass x acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the net force in the vertical direction is: net force = weight = 75 kg x 9.8 m/s^2 = 735 N.
2. What is the magnitude of the normal force on the person?
The magnitude of the normal force on the person is equal to the force exerted by the surface they are in contact with (in this case, the level road). When the person is coasting on a level road, there is no vertical acceleration, so the normal force is equal in magnitude and opposite in direction to the weight. Therefore, the magnitude of the normal force is also 735 N.
3. What is the magnitude of the net horizontal force acting on the earth due to the person?
The magnitude of the net horizontal force acting on the earth due to the person is equal to the force required to cause the person to slow down. This force is due to friction between the skis and the road. Since the person is slowing down, the force of friction acts in the opposite direction to the motion. Without additional information about the specific coefficient of friction between the skis and the road, we cannot determine the exact magnitude of the force. However, we can state that the net horizontal force is equal in magnitude and opposite in direction to the force of friction.
4. If the earth has a mass of 6x10^24 kg, what is the acceleration of the earth in the horizontal direction?
The force exerted by the person on the earth is equal in magnitude and opposite in direction to the force exerted by the earth on the person (Newton's third law of motion). Therefore, the magnitude of the net horizontal force acting on the earth is the same as the magnitude of the force required to cause the person to slow down. To find the acceleration of the earth, we can use the equation: net force = mass x acceleration. Rearranging the formula, we get: acceleration = net force / mass. Since we do not have the exact value of the net force, we cannot calculate the acceleration of the earth without more information.
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