InterviewSolution
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InterviewSolution
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From a point `A` on bank of a channel with still water a person must get to a point `B` on the opposite bank.All the distances are shown in figure.The person uses a boat to travel across the channel and then walks along the bank of point `B`.The velocity of the boat is `v_(1)` and the velocity of the walking person is `v_(2)`.Prove that the fastest way for the person to get from `A` to `B` is to select the angles `alpha_(1)` and `alpha_(2)` in such a manner that A. `(sin alpha_(1))/(sin alpha_(2))=(u_(2))/(v_(1))`B. `(sin alpha_(1))/(sin alpha_(2))=(u_(1))/(v_(2))`C. `(cosalpha_(1))/(cos alpha_(2))=(v_(2))/(v_(1))`D. `(cos alpha_(2))/(cos alpha_(1))=(v_(1))/(v_(2))` |
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Answer» Correct Answer - a `S_(1)=(x)/(sin alpha_(1)),S_(2)=(d-x)/(sin alpha_(2))` `t_(1)=(S_(1))/(v_(1))=(x)/(v_(1)sin alpha_(1))` and `t_(2)=(S_(2))/(v_(2))=(d-x)/(v_(2)sinalpha_(2))` `r=x[(1)/(v_(1)sinalpha_(1))-(1)/(v_(2)sin alpha_(2))]+(d)/(v_(2)sin alpha_(2))` For t be minimum `(dt)/(dx)=0` or `(1)/(v_(1)sin alpha_(1))=(1)/(v_(2)sinalpha_(2)),(v_(1))/(v_(2))=(sin alpha_(2))/(sinalpha_(1))` |
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