Final answer:
Using the work-energy principle, the boat with an initial kinetic energy of 144,000 J will slide a distance of 320 m before stopping due to a constant friction force of 450 N. This answers the question using energy considerations but the calculated distance was not among the provided options.
The correct answer is 320m.
Step-by-step explanation:
To calculate the distance the boat slides on level ground, we can use the work-energy principle, which states that the work done by all forces acting on an object equals the change in kinetic energy of the object. The initial kinetic energy of the boat can be calculated using the formula:
KEi = \(\frac{1}{2}mv^2\), where m is the mass of the boat and v is the initial speed.
For the given boat with a mass of 8,000 kg and an initial speed of 6.00 m/s, the initial kinetic energy (KEi) is:
KEi = \(\frac{1}{2} \times 8000 \times 6.00^2\) = 144,000 J
Since the boat comes to a stop, the final kinetic energy (KEf) is 0 J. The work done by the force of friction (Wf) is the force of friction multiplied by the distance (d) the boat slides, given by:
Wf = -fd, where f is the force of friction and is negative because it opposes the motion.
Since the work done by friction equals the negative change in kinetic energy (because the boat is slowing down), we can equate them:
-fd = -(KEf - KEi)
Solving for distance (d) gives us:
d = \(\frac{KEi}{f}\) = \(\frac{144,000}{450}\) = 320 m
Therefore, the distance the boat slides before coming to a stop is 320 m, which is not one of the options provided in the question, indicating a possible error in the question or answer choices.