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CBSE Class 11-science Answered

A steamer can cross 100m wide river in a time of 10s along the shortest path. If river current speed is 10m/s , then shortest time to cross the river is?
Asked by arunavamitra50 | 31 Oct, 2018, 06:05: PM
answered-by-expert Expert Answer
As shown in figure for shortest path, speed v = begin mathsize 12px style square root of v subscript m superscript 2 space minus space v subscript r superscript 2 end root end style, where vm is steamer's speed and vr is rivers speed.
time taken to cross the river of 100 m wide = begin mathsize 12px style fraction numerator 100 over denominator square root of v subscript m superscript 2 minus v subscript r superscript 2 end root end fraction space equals space fraction numerator 100 over denominator square root of v subscript m superscript 2 space minus space 10 squared end root end fraction space equals space 10 space s end style ..........................(1)
from eqn.(1) we get vm = 10√2 m/s .
 
Shortest time to cross river = 100 / (10√2 ) = 5√2 m/s 
Answered by Thiyagarajan K | 01 Nov, 2018, 04:08: AM
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