Final answer:
Using the centripetal acceleration formula, r = v² / a, and substituting the given values, the radius of the track is calculated to be approximately 12.45 meters, which is not listed in the provided options.
Step-by-step explanation:
To determine the radius of the track on which a sprinter runs with a centripetal acceleration of 5.4 m/s² and at a speed of 8.2 m/s, we can use the formula for centripetal acceleration, which is given by:
a = v² / r
Where a is the centripetal acceleration, v is the velocity, and r is the radius of the circular path. By rearranging the formula to solve for r, we get:
r = v² / a
Substituting the given values into this equation:
r = (8.2 m/s)² / 5.4 m/s²
r = 67.24 m²/s² / 5.4 m/s²
r = 12.45 m
Therefore, the correct answer is not listed in the options provided. The radius of the track should be approximately 12.45 meters.