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CBSE Class 11-science Answered

a person rows a boat across a river making an angle of 60º with downsrtream. what the percentage time he would have saved, hed he crossed the river in the shortest possible time?
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Asked by varsha19sharma86 | 04 Jun, 2020, 02:04: PM
answered-by-expert Expert Answer
l e t s space s a y space t h e space t i m e space t a k e n space b y space m a n space t o space c r o s s space t h e space r i v e r space b e space t subscript 1 w h e n space h e space i s space t r a v e l l i n g space 60 to the power of 0 space w i t h space t h e space d o w n s t r e a m
space t subscript 1 equals fraction numerator d over denominator V S i n 60 to the power of 0 end fraction
space t subscript 1 equals fraction numerator 2 d over denominator V square root of 3 end fraction
I f space h e space h a d space t o space c r o s s space t h e space r i v e r space i n space s h o r t e s t space p o s s i b l e space t i m e space t h e n space t h e space v e l o c i t y space m u s t space b e space e x a c t l y space p e r p e n d i c u l a r space t o space t h e space d i r e c t i o n space o f space f l o w o f space r i v e r.
space t subscript 2 equals d over V
p e r c e n t a g e space o f space t i m e space s a v e d space w o u l d space b e
fraction numerator space t subscript 1 minus space t subscript 2 over denominator space t subscript 2 end fraction
fraction numerator fraction numerator 2 d over denominator V square root of 3 end fraction minus d over V over denominator d over V end fraction
15.47 percent sign
l e t s space s a y space t h e space t i m e space t a k e n space b y space m a n space t o space c r o s s space t h e space r i v e r space b e space t subscript 1 w h e n space h e space i s space t r a v e l l i n g space 60 to the power of 0 space w i t h space t h e space d o w n s t r e a m
space t subscript 1 equals fraction numerator d over denominator V S i n 60 to the power of 0 end fraction
space t subscript 1 equals fraction numerator 2 d over denominator V square root of 3 end fraction
I f space h e space h a d space t o space c r o s s space t h e space r i v e r space i n space s h o r t e s t space p o s s i b l e space t i m e space t h e n space t h e space v e l o c i t y space m u s t space b e space e x a c t l y space p e r p e n d i c u l a r space t o space t h e space d i r e c t i o n space o f space f l o w o f space r i v e r.
space t subscript 2 equals d over V
p e r c e n t a g e space o f space t i m e space s a v e d space w o u l d space b e
fraction numerator space t subscript 1 minus space t subscript 2 over denominator space t subscript 2 end fraction
fraction numerator fraction numerator 2 d over denominator V square root of 3 end fraction minus d over V over denominator d over V end fraction
15.47 percent sign
l e t s space s a y space t h e space t i m e space t a k e n space b y space m a n space t o space c r o s s space t h e space r i v e r space b e space t subscript 1 w h e n space h e space i s space t r a v e l l i n g space 60 to the power of 0 space w i t h space t h e space d o w n s t r e a m
space t subscript 1 equals fraction numerator d over denominator V S i n 60 to the power of 0 end fraction
space t subscript 1 equals fraction numerator 2 d over denominator V square root of 3 end fraction
I f space h e space h a d space t o space c r o s s space t h e space r i v e r space i n space s h o r t e s t space p o s s i b l e space t i m e space t h e n space t h e space v e l o c i t y space m u s t space b e space e x a c t l y space p e r p e n d i c u l a r space t o space t h e space d i r e c t i o n space o f space f l o w o f space r i v e r.
space t subscript 2 equals d over V
p e r c e n t a g e space o f space t i m e space s a v e d space w o u l d space b e
fraction numerator space t subscript 1 minus space t subscript 2 over denominator space t subscript 2 end fraction
fraction numerator fraction numerator 2 d over denominator V square root of 3 end fraction minus d over V over denominator d over V end fraction
15.47 percent sign
Answered by Utkarsh Lokhande | 04 Jun, 2020, 05:23: PM
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