Question

Now, consider the light boat runs ashore on a sand-covered coral reef that has a 5-degree incline. Using energy considerations, calculate the distance the 8,000 kg light boat slides, given that its initial speed is 6.00 m/s and the force of friction acting between the ship and the sand is a constant 450 N.

a) 10 m
b) 20 m
c) 30 m
d) 40 m

Answer 1

The distance the light boat slides is 40 meters.

Step-by-step explanation:

To calculate the distance the light boat slides, we can use the concept of work-energy theorem. The work done by the force of friction can be calculated as the product of the force and the distance. The work done by friction is equal to the change in kinetic energy of the boat. So, we can set up the equation:

Work done by friction = Change in kinetic energy

The work done by friction can be calculated as:

1. Work done by friction = Force of friction * Distance
2. Change in kinetic energy = 0.5 * mass * (final velocity^2 - initial velocity^2)

Equating the two expressions:

Force of friction * Distance = 0.5 * mass * (final velocity^2 - initial velocity^2)

Plugging in the values:

450 N * Distance = 0.5 * 8,000 kg * (0^2 - 6.00 m/s)^2

Simplifying the equation gives:

Distance = 40 meters