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Question

Four persons A,B,C and D at the corners of a square of side X start moving at a constant speed V. Each person maintains a direction towards the person at the next corner. The time the persons take to meet each other is

A
2X3V
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B
X3V
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C
XV
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D
3X4V
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Solution

The correct option is C XV
The motion of A,B,C and D is shown in the figure. They will eventually meet at the center O.

This means the displacement of A will be AO. And his velocity along AO will be
Vcosθ=Vcos45=V/2
Now using Pythagoras theorem on triangle AEO,
AO=X/2
Therefore, time taken to reach O from A will be,
t=AOVcosθ=X/2V/2=XV
This will be the time taken for all A,B,C and D to meet each other.

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