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Question

Two boys running at uniform speeds $$v_1$$ and $$v_2$$ respectively along a straight line path in opposite directions get 9m closer each second. While running along the same direction with their speeds reduced by 50% they get 0.5 m closer each second. the speeds $$v_1$$ and $$v_2$$ are respectively


A
6ms1and3ms1
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B
5ms1and4ms1
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C
5ms1and4.5ms1
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D
5ms1and3.5ms1
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Solution

The correct option is B $$5 ms^{-1} \, and \, 4 ms^{-1}$$
Case (I) When they move in opposite direction 
then,
$${V_1} \leftarrow  \to {V_2}\,\,\,\,{V_1} + {V_2} = 9$$
Case (II) when they move in same direction .
$$\begin{array}{l} \frac { { { V_{ 1 } } } }{ 2 } -\frac { { { V_{ 2 } } } }{ 2 } =\frac { 1 }{ 2 }  \\ { V_{ 1 } }=5\, m/s \\ { V_{ 2 } }=4\, m/s \\ \Rightarrow { V_{ 1 } }-{ V_{ 2 } }=1 \\ \, \, \, \, \, { V_{ 1 } }+{ V_{ 2 } }=9 \end{array}$$
$$\therefore$$ Option $$B$$ is correct.

Physics

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