Final answer:
The bowling ball with a diameter of 18 cm rotates through an angle of approximately 111.02 radians while traveling down a 10-meter lane.
Step-by-step explanation:
The student is asking about the rotation of a bowling ball rolling down a bowling lane. Given the diameter of 18 cm, we can find the radius (r = 9 cm or 0.09 m) to use in our calculations. The ball rolls without slipping at a constant speed of 4.3 m/s down a 10-meter lane. Using the formula distance = radius x angle in radians, we can calculate the number of rotations.
The circumference of the ball (C) is C = 2 x π x radius. Substituting the radius, we get C = 2 x 3.1416 x 0.09 m = 0.5655 m. Now, knowing the total distance traveled by the ball (10 m), we can calculate how many circumferences that entails: 10 m / 0.5655 m = 17.68 rotations or circumferences. Finally, to find the angle in radians, we multiply the number of rotations by 2 x π (since there are 2π radians in one full rotation): 17.68 x 2 x π = 111.02 radians.
Hence, the bowling ball turns through an angle of approximately 111.02 radians as it travels the length of the lane.