Final answer:
To find the tire's rotation frequency in rpm, calculate the tire's circumference and use the car's speed to determine revolutions per second. Then, multiply by 60 to get rpm. The tire's rotation frequency is approximately 703.8 rpm.
Step-by-step explanation:
To solve the mathematical problem completely and determine the tire's rotation frequency in rotations per minute (rpm), we need to use the given diameter of the car tire and the car's velocity. First, we'll convert the diameter to radius by dividing by 2, which gives us a radius of 57.0 cm / 2 = 28.5 cm or 0.285 meters.
The circumference of the tire (the distance it rolls in one complete revolution) is calculated by C = 2πr. So, C = 2π(0.285 m) ≈ 1.79 m. Next, we'll find the number of revolutions per second by dividing the car's speed by the tire's circumference: revolutions per second = 21.0 m/s ÷ 1.79 m/rev ≈ 11.73 rev/s.
To get the rotation frequency in rpm, we multiply the revolutions per second by 60 seconds per minute: frequency (rpm) = 11.73 rev/s × 60 s/min ≈ 703.8 rpm.
Therefore, the tire's rotation frequency is approximately 703.8 rpm when the car is traveling at a speed of 21.0 m/s.