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  • Four persons named K, L, M, N are initially located at the four corners of a square of side d. Now everyone is moving with a constant speed <img alt="v" src="https://entrancecorner.oncodecogs.com/g

Four persons named K, L, M, N are initially located at the four corners of a square of side d. Now everyone is moving with a constant speed v such that K is always moving straight to L, L straight to M, M straight to N, and N straight to K. Four people will meet at the same time.......

Option: 1

\frac{d}{v}


Option: 2

dv


Option: 3

\frac{d^2}{v^2}


Option: 4

\frac{d^2v}{dv^2}


Answers (1)

best_answer

According to symmetry, the four will meet at the centre O, of the square.
At any time along,

Component of Velocity Towards Center along KO

 =v\cos\ 45^{o}=\frac{v}{\sqrt2}

Now, 

distance \ KO\ =\ d\cos\ 45^{o}=\frac{d}{\sqrt2}

Therefore, 

The time taken 

 =\frac{Distance\ KO}{velocity\ along\ KO}=\frac{\frac{d}{\sqrt2}}{\frac{v}{\sqrt2}}

 Now, Time taken = \frac{d}{v}

Posted by

manish

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