Question

Eight particles A, B, C, D, E, F, G and H are originally located at the vertices of regular octagon of side length. At time t =0 second all of them begin to move with constant speed v such that A moves towards B, B moves towards C …. And so on. They will meet after a time interval of

1. t= (root 2 -1)l
________
root 2v
2. t=root 2l
______
(root 2-1)v
3. t= root2l
_____
v

Answer 1

Answer:

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Explanation:

Answer 2

The particles will meet after interval of $\boxed{\frac{\sqrt{2}l}{(\sqrt{2}-1)v}}$

Explanation:

Let the velocity of the particles is v

As shown in the figure

The component of particle at B along AB is $v\sin 45^\circ$

Thus the velocity of A, relative to B

$v_{A/B}=v-v\sin 45^\circ$

$\implies v_{A/B}=v(1-\frac{1}{\sqrt{2}})$

$\implies v_{A/B}=\frac{v(\sqrt{2}-1)}{\sqrt{2}}$

IF the side length of octagon is l

Then the particles are covering this length l with this velocity

Therefore, time taken in meeting

$t=\frac{l}{v(\sqrt{2}-1)/\sqrt{2}}$

$\implies t=\frac{\sqrt{2}l}{(\sqrt{2}-1)v}$

Therefore, option (2) is correct.

Hope this answer is helpful.

Know More:

Q: Six particles are situated at the corners of a regular hexagon of side a and each particle move with a constant speed v in a direction towards the particle at the next corner. calculate the time the particle will take to meet each other.

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