Final answer:
By calculating the tire's circumference, converting the speed to meters per second, and multiplying by the time, we find the total distance covered and then determine the number of wheel revolutions, which is approximately 217,390 revolutions, not matching any of the provided options.
Step-by-step explanation:
To find the angular displacement in revolutions of Formula One race car wheels, we can use the relationship between linear speed, the diameter of the tires, and the distance covered. First, we find the circumference of a tire using the formula:
Circumference = π × diameter
The diameter of the tires is given as 66 cm, which we convert to meters to match the units of the speed (300 km/h):
Diameter in meters = 0.66 meters
Circumference = π × 0.66 meters ≈ 2.07 meters
Next, we convert the average speed to meters per second:
Speed in meters per second = (300 km/h) × (1000 m/km) / (3600 s/h) ≈ 83.33 meters per second
Then we calculate the total distance covered in 1.5 hours:
Total distance = Speed × Time = 83.33 meters per second × 1.5 hours × 3600 seconds/hour ≈ 449,988 meters
Finally, we divide the total distance by the circumference of the tire to find the total revolutions:
Total revolutions = Total distance / Circumference ≈ 449,988 meters / 2.07 meters ≈ 217,390 revolutions
Thus, none of the options a) 7000, b) 8000, c) 9000, or d) 10000 revolutions are correct.