Keep on Chasing!

Classical Mechanics Level 3

A boy runs on a circular path with constant speed u u . Another boy starts from the centre of the circle to catch the first boy. The second boy always moves towards the first one and maintains a speed of v v .

Find the condition such that they both meet after some interval of time.

v ≤ u v \le u v ≥ u v \ge u 2 v ≤ u 2v \le u v = u or v ≥ 2 u v = u \text{ or } v\ge 2u

Rajdeep Dhingra by Rajdeep Dhingra , 20, India

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1 solution

Raghu Alluri
Jul 29, 2019

Well, this is a simple problem in terms of dispensing mathematics and looking at it in terms of physical insight only. If we imagine the second person with speed v v chasing the first person moving in a circle with uniform speed u u , then we can easily see that the second person with speed v v will be tracing out a path that resembles an outward spiral from the center of the circle. This path can be expressed as an equation in terms of polar coordinates if needed for quantitative analysis. However, if we try to extend the spiral into a line we can see it is much greater than the circumference of the circle so therefore the second person must travel at a speed v > = u v >= u to catch up exactly to the first person.

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