A car of mass 1530 kg traveling at 27.0 m/s is at the foot of a hill that rises 115 m in 4.40 km. At the top of the hill, the speed of the car is 6.0 m/s. Find the average power delivered by the car's engine, neglecting any frictional losses

I got 8145.7 watts but that is not the correct answer.

total energy at top

= (1/2)(1530)(36) + 1530(9.81)(115)

total energy at bottom
= (1/2)(1530)(27)^2

work done = energy at top - energy at bottom

average velocity = (27+6)/2
time = 4400/average velocity

power = work done/time

the difference in total energy (kinetic plus potential) at the base and the top; is the energy input from the engine

the ascent time is the average speed, (top + bottom) / 2; divided by the 4.40 km distance

energy / time equals power

your answer has 5 sig figs. but all the data is only 3

To find the average power delivered by the car's engine, we need to calculate the work done by the engine and divide it by the time taken to do that work. Here's how you can solve it step by step:

Step 1: Calculate the work done by the engine:
Work = Change in kinetic energy + Change in potential energy

The change in kinetic energy (ΔKE) can be found using the formula:
ΔKE = 1/2 * m * (v2^2 - v1^2),
where m is the mass of the car, v1 is the initial velocity, and v2 is the final velocity.

Substituting the given values:
ΔKE = 1/2 * 1530 kg * ((6.0 m/s)^2 - (27.0 m/s)^2)
ΔKE = 1/2 * 1530 kg * (-621 m^2/s^2)
ΔKE = -471,795 J

Note: The negative sign indicates that there is a decrease in kinetic energy.

The change in potential energy (ΔPE) can be found using the formula:
ΔPE = m * g * h,
where m is the mass of the car, g is the acceleration due to gravity (9.8 m/s^2), and h is the height difference.

Converting the given height difference from km to meters:
h = 115 m + 4.40 km * 1000 m/km
h = 115 m + 4400 m
h = 4515 m

Substituting the values:
ΔPE = 1530 kg * 9.8 m/s^2 * 4515 m
ΔPE = 66,158,010 J

The total work done by the engine:
Work = ΔKE + ΔPE
Work = -471,795 J + 66,158,010 J
Work = 65,686,215 J

Step 2: Calculate the time taken (t):
The time taken (t) can be found using the average speed (v_avg) and the distance (d) traveled:
t = d / v_avg

Given:
v_avg = (v1 + v2) / 2
v1 = 27.0 m/s
v2 = 6.0 m/s
d = 4.40 km

Converting the distance from km to meters:
d = 4.40 km * 1000 m/km
d = 4400 m

Calculating the average speed:
v_avg = (27.0 m/s + 6.0 m/s) / 2
v_avg = 33.0 m/s / 2
v_avg = 16.5 m/s

Calculating the time taken:
t = 4400 m / 16.5 m/s
t ≈ 266.67 s

Step 3: Calculate the average power (P):
Average Power (P) = Work / Time
P = 65,686,215 J / 266.67 s
P ≈ 246,408.6 Watts

So, the average power delivered by the car's engine, neglecting any frictional losses, is approximately 246,408.6 Watts.