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© GC Shiba
Crossing river:
Suppose a swimmer of potential v wants to cross
the river which is flow with U in
❖ Shortest time and
❖ Along shortest route
Let the swimmer enter the river by making an
angle of with vertical. The velocity v of
swimmer can be resolved into components
and along vertical and horizontal direction.
maintains vertical motion whereas maintain horizontal motion.
, ( ) =
= … … … . . . ( ) ℎ ℎ .
ℎ ℎ
. . = ±1
∴ = 0°.
0
It means swimmer must swim along the vertical or by making 90 with the flow of
river.
Along shortest river: The swimmer can swim along shortest route as well if the
effect of water on swimmer is minimal. It is only possible if the horizontal
component of swimmer balances the flow of river.
i.e.: = , = −1 ( )
This is the required direction to cross the river along shortest route.
14 Mechanics
