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Question

Three persons P, Q and R of same mass travel with same speed u along an equilateral triangle of side 'd' such that each one faces the other always. After how much time will they meet each other.
1213291_c420b7652b884ef78f1ea2fee3dd42b4.PNG


A
du seconds
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B
2d3u seconds
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C
2d3u seconds
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D
d3u seconds
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Solution

The correct option is B $$\dfrac{2d}{3u}$$ seconds
$$QC=\dfrac { 2 }{ 3 } \sqrt { { a }^{ 2 }-{ \left( \dfrac { d }{ 2 }  \right)  }^{ 2 } } =\dfrac { d }{ \sqrt { 3 }  } $$
so time taken for QC becomes zero
$$=\dfrac { \dfrac { d }{ \sqrt { 3 }  }  }{ u\quad \cos { { 30 }^{ \circ  } }  } $$
 $$=\dfrac { \frac { d }{ \sqrt { 3 }  }  }{ u\times \dfrac { \sqrt { 3 }  }{ 2 }  } $$
 $$=\dfrac { 2d }{ 3u } seconds$$


Physics

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