Final answer:
To find the tire's rotation frequency in rpm, calculate the tire's circumference from its diameter, then determine how many rotations occur in one second by dividing the car's speed by the tire's circumference. Finally, multiply the rotations per second by 60 seconds to convert to rpm. None of the student's provided options match the correct answer of 704.4 rpm.
Step-by-step explanation:
The student has asked about the rotation frequency of a car tire given its diameter and the car's speed. To calculate the tire's rotation frequency, we'll first find the tire's circumference, since the circumference is the distance covered in one rotation. Using the diameter (d = 57.0 cm), we calculate the circumference (C) as C = πd. Therefore, the circumference is approximately 178.88 cm or 1.7888 m. The car's speed is given as 21.0 m/s, so in one second, the tire covers 21.0 meters of road.
To determine how many rotations occur in one second, we divide the car's speed by the tire's circumference: rotations per second = speed/circumference, which gives us approximately 11.74 rotations per second. Now, to find the rotation frequency in rotations per minute (rpm), we multiply this value by 60, yielding a result of 704.4 rpm. Comparing this result to the options provided by the student, none of them match; however, we can guide the student through the correct method to find the answer.