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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 / tarun
The reason previous answer is wrong is because at any given
point of time they are not moving along the diagonal of the
square. They end up traversing a quarter-circular arc - this
can be verified by looking at the tangents on the four
circular arcs at any given point of time and they will show
how each ant is moving instantaneously in a straight line in
the direction of its neighbor. Therefore the total distance
covered is 1/4(2*pi*r) where r=1, or pi/2, and so the total
time taken is also pi/2 units.
| Is This Answer Correct ? | 3 Yes | 23 No |
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