Answer:
head straight across the river (perpendicular to the bank).
Explanation:
To cross the river in the shortest time first your velocity should be relative to the earth has to have the largest possible component to the bank
suppose,
S be the swimmer
E be the earth
W be the water
[tex]u_{x/y}[/tex] be the velocity of X relative to Y
resultant velocity relative to E will be:
[tex]u_{S/E}=u_{S/W}+u_{W/E}[/tex]
[tex]u_{W/E}[/tex] is parallel to the bank so,
[tex]u_{S/E}[/tex] has its largest component perpendicular to the bank when [tex]u_{S/W}[/tex] is in that direction
so to cross the river in the shortest time you should straight across the current will then carry you downstream so your path relative to the earth is directed at angle downstream
