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Four persons K, L, M, and N are initially at the four corners of a square of side d. Each persons now moves with a uniform speed v in such a way that K always moves directly towards L, L directly towards M, M directly towards N and N directly toward K. The four persons will meet at a time ..........??
Each of them will meet at centre of the square as shown in figure.. After every unit time , they will be forming a square..
Let the centre be O. Now distance ON will be d/√2.
N is moving towards K and angle KNO is 45 degree.The component of velocity of K which will Cover the distance ON is" v cos 45= v/√2".
Now, time taken, t to cover the distance ON will be = (d/√2)/(v/√2)="d/v". (Ans.) Similarly, we can solve for any regular closed figure... like triangle, hexagon etc...
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