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 by 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 \[{{t}^{2}}({{v}^{2}}-v_{1}^{2})={{a}^{2}}\] \[\therefore \] \[t=\sqrt{\frac{{{a}^{2}}}{({{v}^{2}}-v_{1}^{2})}}\]You need to login to perform this action.
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