Saturday, 27 October 2012

Jogging & Math: "Jogging – Circular path"

One morning while I was jogging around my apartment complex, I got a doubt. Let us suppose that I am jogging in a circular path and another person is also jogging in a parallel circular path (with a different radius). What is the difference between the distances travelled by me and the other person? Even if the difference between the radii is small, the difference between total distances travelled is more. why so?  what is the underlying concept here?

Let us consider that person ‘A’ is jogging in outer circle of radius ‘R’ and ‘B’ is jogging in an inner circle of radius ‘r’. Obviously R > r. The distance travelled by A in one round is nothing but the length of circumference of the circular path he travelled.

The distance travelled by A = 2πR
Similarly, the distance travelled by B = 2πr
Difference of the distances = 2π(R-r).

The difference of distances travelled in one round is multiplied by a factor ‘2π’ to the difference of radii of the two circular paths. If we consider the approximate value of ‘π’ as 3.14, the multiplying factor becomes ‘6.28’. This means, if B is jogging at 2 ft lesser radial length to that of A, the total distance travelled by B in one round is around 12 ft less than that of A. This is only for one round. If we consider for 10 rounds, the difference becomes 120 ft.

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