Consider a baseball player sliding toward home plate on level ground. Using energy considerations, calculate the distance the 75 kg player slides to a stop if his initial speed is 4.75 m/s and the friction force against him is a constant 440 N.

a) What is the distance the player slides to a stop on level ground?

A. 36.11 meters
B. 27.78 meters
C. 19.82 meters
D. 14.75 meters

Suppose that, because this is a minor league field, the ground is not level but actually slopes upward at a 4.5-degree angle above the horizontal. How far up this slope will the player slide?

b) How far up the slope will the player slide?

A. 1.69 meters
B. 3.02 meters
C. 2.45 meters
D. 4.13 meters

If the baseball player were to slide down this incline, how far will he travel before coming to a stop?

c) How far will he travel down the incline before stopping?

A. 1.69 meters
B. 3.02 meters
C. 2.45 meters
D. 4.13 meters

The player would slide approximately 0.96 meters on level ground. The exact distance on an upward slope would require more information, such as the friction coefficient, due to the extra gravitational component competing with his motion.

Explanation:

The question asks us to use the principles of work-energy theorem. When the baseball player slides to a stop, he is losing kinetic energy due to friction. Now, calculating the work done by friction, which is equal to the initial kinetic energy of the player, we get:

W_fd = 0.5 * m * v2

Where m is the mass of the player (75 kg), v is the speed (4.75 m/s).
So, W_fd = 0.5 * 75 * (4.75)^2 = 423.7 J.

Next, we set this work equal to the friction work done, which is the friction force times the distance, to solve for the distance:

W_fd = Ff * d

Solving this equation, we find that the distance d (a sliding stop on flat ground) = 0.96 meters (which is not an option in your given choices). For the part with the inclined slope, if the slope is not frictionless, then the distance will further reduce due to an additional component of gravity acting against the motion. Using trigonometry and again using the principle of conservation of energy, the distance on the slope can be determined. But we will need a friction coefficient to continue our calculations.

Learn more about Kinetic Energy and Friction here:

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