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Classical Mechanics Level 4

Six particles are situated at the corners of a regular hexagon of side 6 cm 6\text{ cm} move at a constant speed 0.5 cm/s 0.5 \text{ cm/s} . Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other.


The answer is 24.

Mohit Gupta by Mohit Gupta , 20, India

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1 solution

Swapnil Das
Apr 16, 2017

By symmetry, the particles shall converge at the center of the hexagon.

Component of velocity along the center of the hexagon is v cos ⁡ π 6 = v 2 v\cos\frac{\pi}{6}= \frac{v}{2} , which always remains the same.

Time is the ratio of distance travelled and the speed travelling that distance. The distance between vertex of the hexagon and its center is a a .

τ = a v 2 = 2 a v = 24 s \tau = \frac{a}{\frac{v}{2}}= \frac{2a}{v}= 24 s

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