Final answer:
The power of the car is approximately 66.7 horsepower.
Step-by-step explanation:
To calculate the power of the car, we need to use the formula:
Power = Work / Time
First, we need to calculate the work done by the car to climb the mountain. The work done is equal to the gravitational potential energy gained by the car:
Work = mgh
Where m is the mass of the car (1,442 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the mountain (653 meters).
Now, we can calculate the power:
Power = Work / Time
Given that it takes 2.308 minutes to climb the mountain, we need to convert it to seconds:
Time = 2.308 minutes * 60 seconds/minute = 138.48 seconds
Substituting the values into the formula:
Power = (mgh) / Time
Power = (1,442 kg * 9.8 m/s^2 * 653 m) / 138.48 seconds
Power = 6,923,872 J / 138.48 s
Finally, we can convert the power from joules/second to horsepower:
1 horsepower = 746 watts
Power (in horsepower) = Power (in watts) / 746
Substituting the value:
Power (in horsepower) = 6,923,872 J / 138.48 s / 746
Power (in horsepower) ≈ 66.7 hp