# 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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