A power boat of mass 475 kg is cruising at a constant speed of 8.9 m/s. The propeller provides a drive force of 770 N. The driver of the boat shuts off the engine, and the boat coasts to a halt. Assume -- contrary to fact -- that the resistive force due to the water is constant, independent of the boat's speed.

(a) How far does the boat coast?

(b) How much time does it take for the boat to come to rest after the engine is turned off?

friction force is 770N.
KEinitial=frictionforce*distance
solve for distance.

The average speed is 8.9/2 m/s. You know the distance
time=distance/avgspeed.

To determine the distance the boat coasts, we can use the concept of kinetic energy.

The initial kinetic energy (KE) of the boat can be calculated using the work-energy principle: KE = work done against friction force.

Given that the friction force is 770 N, we can write the equation:
KE_initial = friction force * distance

Rearranging the equation to solve for distance:
distance = KE_initial / friction force

Since the boat is cruising at a constant speed of 8.9 m/s, the average speed during the coasting period can be considered as 8.9/2 m/s.

To determine the time it takes for the boat to come to rest after the engine is turned off, we can use the average speed and distance formula.

We know the distance from the previous calculation. Now we can write the time equation as:
time = distance / average speed

By substituting the given values into these equations, you can find both the distance the boat coasts and the time it takes for the boat to come to rest after the engine is turned off.