A) 2.3
B) 1.8
C) 0.5
D) 0.2
Correct Answer: B
Solution :
[b] Suppose the stream velocity is \[{{\text{v}}_{\text{s}}}\text{=v}\], then the velocity of each boat with respect to water is \[{{\text{v}}_{b}}=1.2\text{ v}\]. Let each boat travel a distance\[\ell \]. |
Then for boat A, time of motion \[{{\tau }_{A}}=\frac{\ell }{{{v}_{b}}+{{v}_{s}}}+\frac{\ell }{{{v}_{b}}-{{v}_{s}}}\] |
\[=\left[ \frac{\ell }{1.2\,v+v}+\frac{\ell }{1.2\,v-v} \right]=\frac{60\text{ }\ell }{11\,v}\] ?..(i). |
For the boat B, time of motion \[{{\tau }_{B}}=\frac{\ell }{\sqrt{{{v}_{b}}^{2}-{{v}_{s}}^{2}}}+\frac{\ell }{\sqrt{{{v}_{b}}^{2}-{{v}_{s}}^{2}}}=\frac{2\ell }{\sqrt{{{v}_{b}}^{2}-{{v}_{s}}^{2}}}\] ?(ii) |
\[=\frac{2\ell }{\sqrt{{{\left( 1.2\,v \right)}^{2}}-{{v}^{2}}}}=\frac{3.01\text{ }\ell }{v}\] |
The ratio \[\frac{{{\tau }_{A}}}{{{\tau }_{B}}}=\frac{\left( 60\,\ell /11\,v \right)}{\left( 3.01\,\,\ell /v \right)}\approx 1.8\] |
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