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A steam boat goes across a lake and comes back (i) on a quite day when the water is still and (ii) on a rough day when there is a uniform current so as to help the journey onwards and to impede the journey back. If the speed of the launch on both days was same, the time required for complete journey on the rough day, as compared to the quite day will be

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less

same

None of these

answer is A.

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Detailed Solution

Here, $t_{1} = \frac{x}{v} + \frac{x}{v} = \frac{2 x}{v}, t_{2} = \frac{x}{v + ω} = \frac{x}{v - ω} + \frac{2 x v}{v^{2} - ω^{2}}$

or $t_{2} = \frac{2 x v}{v^{2} (1 - \frac{ω^{2}}{v^{2}})} = \frac{2 x}{v (1 - \frac{ω^{2}}{v^{2}})}$

or $t_{2} = \frac{t_{1}}{1 - \frac{ω^{2}}{v^{2}}} o r t_{2} > t_{1}$

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