A car of mass 1410 kg traveling at 26 m/s is at the foot of a hill that rises 115 m in 4 km. At the top of the hill, the speed of the car is 14 m/s. Find the average power delivered by the car's engine, neglecting any frictional losses.

To find the average power delivered by the car's engine, we can use the work-energy principle. The work done by the engine is equal to the change in kinetic energy of the car, and the average power can be calculated by dividing the work done by the time taken.

First, let's calculate the work done by the engine to bring the car from the foot of the hill to the top.

The work done is given by the formula:

Work = change in kinetic energy = (1/2) * mass * (final velocity^2 - initial velocity^2)

Given:
Mass (m) = 1410 kg
Initial velocity (u) = 26 m/s
Final velocity (v) = 14 m/s

Work = (1/2) * 1410 kg * (14 m/s)^2 - (26 m/s)^2

Now let's calculate the distance traveled by the car from the foot of the hill to the top.

Given:
Height of the hill (h) = 115 m
Distance traveled (s) = 4 km = 4000 m

The work done against gravity is equal to the potential energy gained by the car:

Potential Energy = mass * gravity * height

Potential Energy = 1410 kg * 9.8 m/s^2 * 115 m

Now, we know that the work done by the engine is equal to the work done against gravity. Therefore,

Work = Potential Energy

Now, let's calculate the average power delivered by the engine.

Average Power = Work done / Time taken

To find the time taken, we need to know the average speed of the car. Average speed is given by:

Average Speed = Total distance / Time

The total distance traveled is the sum of the distance covered going up the hill and coming down the hill. Given that the distance up the hill is 4000 m, the total distance is:

Total Distance = 4000 m + 4000 m = 8000 m

Now, we can calculate the time taken:

Time taken = Total distance / Average Speed

Finally, we can calculate the average power delivered by the engine:

Average Power = Work done / Time taken

By plugging in the values, we can calculate the average power delivered by the car's engine.