Answer :
Final answer:
The distance the baseball player slides to a stop on level ground is approximately 36.11 meters. When sliding up a 4.5° slope, the player will slide approximately 2.45 meters up the slope.
Explanation:
To calculate the distance the baseball player slides to a stop on level ground, we need to consider the work done by the friction force. The work done by the friction force is equal to the initial kinetic energy of the player. Using the work-energy principle, we can set up the equation:
Work friction = Initial kinetic energy
Fd = 0.5 * m * v^2
where F is the friction force, d is the distance the player slides, m is the mass of the player, and v is the initial velocity of the player. Rearranging the equation, we can solve for d:
d = (0.5 * m * v^2) / F
Plugging in the given values, we have:
d = (0.5 * 75 kg * (4.75 m/s)^2) / 440 N
d ≈ 36.11 meters
So, the distance the player slides to a stop on level ground is approximately 36.11 meters.
Now, let's consider the player sliding up a 4.5° slope. We need to calculate how far up the slope the player will slide. In this case, we can use the same equation as before, but now the work done by the friction force will also be used to increase the potential energy of the player:
Work friction = Change in kinetic energy + Change in potential energy
Fd = (0.5 * m * vf^2) - (0.5 * m * vi^2) + m * g * h
where vf is the final velocity of the player, vi is the initial velocity of the player, and h is the vertical displacement. Since the player comes to a stop, vf is 0. Solving for h:
h = (Fd + 0.5 * m * vi^2) / (m * g)
Using the given values:
h = (440 N * d + 0.5 * 75 kg * (4.75 m/s)^2) / (75 kg * 9.8 m/s^2)
h ≈ 2.45 meters
So, the player will slide approximately 2.45 meters up the slope.
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