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There are four dogs/ants/people at four corners of a square
of unit distance. At the same instant all of them start
running with unit speed towards the person on their
clockwise direction and will always run towards that target.
How long does it take for them to meet and where?
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Answer Posted / venkat
answer # 3 is almost correct. they will meet at the center however the time they would take according to my calculation is not 1 unit of time but less than 1 unit of time [approx 0.78 unit of time]. the reason being since all of the four are moving tracing arcs toward the center of the square, the distance of the arc is definitely less than 1 unit [little more than half the diagonal distance, half the diagonal distance is about = 0.707 unit]. the question says speed and not velocity. speed is distance traversed / time taken to cover the distance. Here distance is the length of the arc [0.78 unit] to be precise and not even half the diagonal distance [0.70 unit], leave alone the initial distance [1 unit] between the two people. arc length that I got was using this formula: (2 x pi x 0.5) / 4 = 0.78. Further 1 unit speed = 0.78 unit / time and it follows time = 0.78 unit of time.
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