A person- intending to cross a river by the shortest path- starts an angle alpha with the downstream- If the speed of the person is than that of water current- show that alpha must be obtuse-

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Toppr Admin · Accepted Answer

Vw- velocity of watervsw- velocity of swimmer w-r-t watervs- velocity of swimmer-xA0-tan-x3B2-vsvwas- vs-lt-vw-x2234- tan-x3B2-lt-1-x3B2- acute-x27F9-x3B1-obtuse-

A person, intending to cross a river by the shortest path, starts at an angle $α$ with the downstream. If the speed of the person is less than that of water current, show that $α$ must be obtuse.

$v_{w} =$ velocity of water
$v_{s w} =$ velocity of swimmer w.r.t water
$v_{s} =$ velocity of swimmer
$tan β = \frac{v_{s}}{v_{w}}$
as, $v_{s} < v_{w}$
$∴$ $tan β < 1$
$β =$ acute $⟹ α =$ obtuse.

A person, intending to cross a river by the shortest path, starts at an angle α with the downstream. If the speed of the person is less than that of water current, show that α must be obtuse.

vw= velocity of watervsw= velocity of swimmer w.r.t watervs= velocity of swimmer tanβ=vsvwas, vs<vw∴ tanβ<1β= acute⟹α=obtuse.

A person, intending to cross a river by the shortest path, starts at an angle $α$ with the downstream. If the speed of the person is less than that of water current, show that $α$ must be obtuse.

$v_{w} =$ velocity of water
$v_{s w} =$ velocity of swimmer w.r.t water
$v_{s} =$ velocity of swimmer
$tan β = \frac{v_{s}}{v_{w}}$
as, $v_{s} < v_{w}$
$∴$ $tan β < 1$
$β =$ acute $⟹ α =$ obtuse.