A) \[\frac{a}{\sqrt{{{v}^{2}}+v_{1}^{2}}}\]
B) \[\sqrt{\frac{{{a}^{2}}}{{{v}^{2}}-v_{1}^{2}}}\]
C) \[\frac{a}{(v-{{v}_{1}})}\]
D) \[\frac{a}{(v+{{v}_{1}})}\]
Correct Answer: B
Solution :
Distance covered by boy A in time t |
\[AC=vt\] ....(i) |
Distance covered y boy B in time t |
\[BC={{v}_{1}}t\] (ii) |
Using Pythagorus theorem |
\[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\] |
or \[{{(vt)}^{2}}={{a}^{2}}+{{({{v}_{1}}t)}^{2}}\] |
or \[{{v}^{2}}{{t}^{2}}-v_{1}^{2}{{t}^{2}}={{a}^{2}}\] |
or \[{{t}^{2}}({{v}^{2}}-v_{1}^{2})={{a}^{2}}\] |
\[\therefore \] \[t=\sqrt{\frac{{{a}^{2}}}{({{v}^{2}}-v_{1}^{2})}}\] |
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