A car of mass 1490 kg traveling at 22 m/s is at the foot of a hill that rises 115 m in 3.2 km. At the top of the hill, the speed of the car is 12 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 need to calculate the work done and divide it by the time taken.

1. Calculate the work done:
Work = Force x Distance

Since the only force acting on the car is the force of gravity, we can calculate it using the formula:

Force = Mass x Acceleration due to gravity

Acceleration due to gravity is approximately 9.8 m/s².

Force = 1490 kg x 9.8 m/s²
= 14,582 N

Next, we need to calculate the distance traveled by the car along the incline. The height of the hill is given as 115 m, and the horizontal distance traveled is 3.2 km. We can calculate the inclined distance using trigonometry:

Inclined distance = sqrt((horizontal distance)² + (height)²)
= sqrt((3.2 km)² + (115 m)²)

Converting the horizontal distance to meters:

Horizontal distance = 3.2 km x 1000 m/km
= 3200 m

Inclined distance = sqrt((3200 m)² + (115 m)²)
= sqrt(10,240,000 m² + 13,225 m²)
= sqrt(10,253,225 m²)
≈ 3204.59 m

Now we can calculate the work done by the car:

Work = Force x Distance
= 14,582 N x 3204.59 m
≈ 46,874,468 J

2. Calculate the time taken:
Time = Total distance / Average velocity

The total distance traveled by the car is the horizontal distance plus the height of the hill:

Total distance = horizontal distance + height of the hill
= 3200 m + 115 m
= 3315 m

The time taken can be calculated as:

Time = 3315 m / ((22 m/s + 12 m/s) / 2)
= 3315 m / (34 m/s / 2)
= 3315 m / 17 m/s
≈ 195 s

3. Calculate the average power:
Average Power = Work / Time

Average Power = 46,874,468 J / 195 s
≈ 240,869 W

Therefore, the average power delivered by the car's engine is approximately 240,869 W.

To find the average power delivered by the car's engine, we need to calculate the work done by the car and divide it by the time it took to do that work.

First, let's find the work done by the car. Work is equal to the change in kinetic energy (KE) plus the change in potential energy (PE):

Work = ΔKE + ΔPE

To find the change in kinetic energy, we need to calculate the initial and final kinetic energies of the car.

Initial kinetic energy (KEi) = 1/2 * mass * (initial velocity)^2
Final kinetic energy (KEf) = 1/2 * mass * (final velocity)^2

Next, we need to calculate the change in potential energy. The car has gone up a hill, so it has gained potential energy. The change in potential energy is given by:

ΔPE = mass * g * height

where g is the acceleration due to gravity (approximately 9.8 m/s^2) and height is the change in elevation.

Now, we can calculate the work done by the car:

Work = ΔKE + ΔPE
= (KEf - KEi) + (mass * g * height)

Since the question mentions neglecting any frictional losses, there is no work done against friction.

Finally, we divide the work by the time it took to do that work to find the average power:

Average power = Work / time

Since the question does not specify the time it took for the car to go up the hill, we cannot directly calculate the average power.