Will they ever meet?

Classical Mechanics Level 4

Consider three particles P , Q , R P,Q,R which are situated at the vertices of equilateral triangle A B C ABC of side 1 m 1\text{ m} .Each of the particles move with constant speed 1 m/s 1 \text{ m/s} . P P always has its velocity along A B AB , Q Q always has its velocity along B C BC , R R always has its velocity along C A CA . At what time in seconds will the particles meet each other?

  • If you think that they will never meet , prove it and enter the answer as 1.1.

  • If you think that they will meet at infinity , prove it and enter the answer as 2.2.


The answer is 0.666.

Nihar Mahajan by Nihar Mahajan , 20, India

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2 solutions

Aakash Khandelwal
Jul 18, 2015

2a/3v for generalisation

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Nelson Mandela
Jul 18, 2015

Let us consider AB. Then using the concept of relative velocity and condition for collision, the velocities along line joining A and B will cause their collision.

There are 2 velocities along AB. The velocity of A(1m/s) along AB and parallel component of velocity of B along AB which is 1 x cos(60)[equilateral triangle].

also, these velocities are towards each other so they will collide.

Relative velocity will be 1 + 1cos(60) = 3/2(as both are contributing to collision).

so time = distance/speed = 1/(3/2) = 2/3 = 0.66.

[NOTE- also try this for a n-sided polygon]

1 Helpful 0 Interesting 0 Brilliant 0 Confused

@Nihar Mahajan : a generalized version of this problem is there in H.C.Verma - Concepts of Physics (Part -1)

Vishwak Srinivasan - 5 years, 11 months ago

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Also in Irodov, I guess.

Swapnil Das - 5 years, 11 months ago

Particle meet each other would be best described with time of 0 s.

To collide, resultant of vector sum cannot be detached away.

Your collision is just pure imagination of velocity component with one of each main resultant, which cannot be real.

The definition of particles meet each other had been too personal that you didn't tell.

Not that your thinking is absolutely wrong but to deny for never meet and 0 s to see each other are not right thing to do. To guess your mind, we have to take the third trial for a risk of getting wrong of which I usually try up to 2nd trial only when I cannot be certain of the answer obtainable by me. My third trial was "1.1." and fortunately not accepted. How were I able to answer this question correctly?

Lu Chee Ket - 5 years, 7 months ago

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