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. $6m{s}^{-1}and3m{s}^{-1}$
• B. $5m{s}^{-1}and4m{s}^{-1}$
• C. $5m{s}^{-1}and4.5m{s}^{-1}$
• D. $5m{s}^{-1}and3.5m{s}^{-1}$

Answer 1

The correct option is B $5m{s}^{-1}and4m{s}^{-1}$

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 .

$\begin{array}{c}\frac{V_1}{2}-\frac{V_2}{2}=\frac{1}{2}\\ V_1=5m/s\\ V_2=4m/s\\ \Rightarrow V_1-V_2=1\\ V_1+V_2=9\end{array}$

$\therefore$ Option $B$ is correct.