Question

in track, the second lane from the inside of the track is longer than the inside lane. use this information to explain why, in running events that require a complete lap of the track, runners are lined up at the starting blocks as shown in the accompanying figure.
click the icon to view the track figure

choose the correct explanation for why the starting blocks are at the locations shown in the figure.
a. the outer curve has a greater radius and a correspondingly greater distance (that is, arc length) to run. to compensate for the extra distance, the runner in the outer lane is given an apparent head start.
b. the outer curve has a greater radius and a correspondingly greater distance (that is, arc length) to run. to compensate for the extra distance, the runner in the outer lane is provided the opportunity to get a better view of the track in order to avoid obstacles.
c. the inner curve has a greater radius and a correspondingly greater distance (that is, arc length) to run. to compensate for the extra distance, the runner in the inner lane is provided the opportunity to get a better view of the track in order to avoid obstacles.
d. the inner curve has a greater radius and a correspondingly greater distance (that is, arc length) to run. to compensate for the extra distance, the runner in the inner lane is given an apparent head start

Explanation:

The formula for arc length is \(s = r\theta\) (where \(s\) is arc length, \(r\) is radius, and \(\theta\) is the central angle in radians). In a track, the central angle \(\theta\) for a full - lap curve is the same for all lanes. Since the outer lane has a greater radius \(r\), its arc length \(s\) (the distance to run along the curve) is greater. To make the total distance of a full - lap race equal for all runners (despite the different lane lengths), the runner in the outer lane is given an apparent head start. Option B is incorrect because getting a better view is not a reason for the starting - block placement. Options C and D are incorrect because the inner lane has a smaller radius, not a greater one.

Answer:

A. The outer curve has a greater radius and a correspondingly greater distance (that is, arc length) to run. To compensate for the extra distance, the runner in the outer lane is given an apparent head start.