Final answer:
The angular velocity of the truck's tires is approximately 76.2 rad/s, and when converted to revolutions per minute, it is approximately 727.3 rev/min. Therefore, the correct answer is A.
Step-by-step explanation:
To find the angular velocity of the rotating tires in radians per second (rad/s), we use the relationship between linear velocity (v), the radius of the tire (r), and the angular velocity (ω), which is v = ωr. In this case, the linear velocity (v) is 32.0 m/s and the radius (r) is 0.420 m. This gives:
ω = v / r = 32.0 m/s / 0.420 m = 76.19 rad/s (approximately).
To convert the angular velocity to revolutions per minute (rev/min), you must first convert radians per second to revolutions per second by dividing by 2π (since there are 2π radians in a revolution). You then multiply by 60 to convert from seconds to minutes:
rev/s = ω / (2π) = 76.19 rad/s / (2π) = 12.12 rev/s (approximately).
rev/min = rev/s × 60 = 12.12 rev/s × 60 = 727.2 rev/min (approximately).
Therefore, the correct answer is A. 76.2 rad/s, 727.3 rev/min.