He is Invisible(Original)

8 particles are situated at corners of regular octagon of side a. Each particle maintain a direction towards the particle at the next corner with a constant speed v, simultaneously a \(9^{th}\) particle(invisible to other 8 particles) starts at rest from the mid point of the side and move perpendicular to side with constant acceleration.

The acceleration of the \(9^{th}\) particle so that all the particles meet together at a point can be written as

\[\frac{a(\sqrt{b} - c)}{d}\]

Where 'b' is square free and \(\frac{a}{d}\) is in simplest form.

Then find

\(a + b + c + d\)

Details and Assumptions

  • Neglect any other collision

  • a = 7 (side length)

  • v = 4

  • All values are in SI unit


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