A boat takes 2 hours to travel 8 km and back in still water lake. With water velocity of `4 km h ^(-1),` time taken for going upstream of 8 km and coming back is

Explanation

`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))`