Making races equal

Classical Mechanics Level 2

If you ever watch track and field at the Olympics, you'll notice that the starting points of the runners are not even if the race is run on a curve and the runners have to run in lanes. This is to offset the fact that the distances along each lane are unequal on a curve. To see this effect, consider two runners, each of whom runs at a speed of $7~\mbox{m/s}$ . The runners run on a circular track. The radius of the inside lane is $50~\mbox{m}$ , and the radius of the outside lane is $51~\mbox{m}$ . By how many seconds will the inside runner beat the outside runner if they each run once around the track?

The answer is 0.897.

1 solution

David Mattingly Staff
May 13, 2014

The distance the outside runner travels is $2 \pi \times 51$ which takes them $45.777~\mbox{seconds}$ . The distance the inside runner travels is $2 \pi \times 50$ , which takes $44.88~\mbox{seconds}$ . The difference is therefore $0.897~\mbox{seconds}$ .

Making races equal

The answer is 0.897.

1 solution

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