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A boat takes 2 hours to travel 8 km and ...

A boat takes `2 hours` to travel `8 km` and back in still water lake.With water velocity of `4 kmph`,the time taken for going upstream of `8km` and coming back is

Text Solution

Verified by Experts

`u cos alphat=D` …(i)
`u cos alpha t-1/2 g t^(2)=-H` …(ii)
`rArr t=(2u sin alpha+-sqrt(u^(2) sin^(2)alpha+2gH))/g=D/(u cos alpha)`
`h=((u sin alpha)^(2))/(2g)=(D^(2)tan^(2)alpha)/(4(H+D tan alpha))`
`:. H_("max")=h+H=H+(D^(2)tan^(2)alpha)/(4(H+D tan alpha))`
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