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CBSE Class 11-science Answered

a boat is moving in a river with velocity 6km/h ,(1)upstream(2)downstream .what is the resultant velocity of th boat if the velocity of the flow of water is 4km/h.
Asked by rajkumarimaravi85 | 17 Aug, 2018, 09:03: AM
answered-by-expert Expert Answer
Hi, you may find the answer in one of the similar queries posted to us by a student.
 
Question: 
 
A man rows directly across a flowing river in time t1 and rows an equal distance down the stream in time t2 . If u is the speed of the man in still water and v that of stream, then find the ratio of t1and t2 in terms of u and v . Also mention the formulae of vectors  used .
 
Answer:
 
For solving the below question:
A man rows directly across a flowing river in time t1 and rows an equal distance down the stream in time t2 . If u is the speed of the man in still water and v that of stream, then find the ratio of t1 and t2 in terms of u and v . Also mention the formulae of vectors  used .
 
 
 
We know that 
begin mathsize 12px style Speed equals Distance over Time Time equals Distance over Speed The space ratio space of space time space straight t subscript 1 space and space straight t subscript 2 space will space be fraction numerator space straight t subscript 1 over denominator space straight t subscript 2 end fraction equals fraction numerator begin display style bevelled fraction numerator space straight d subscript 1 over denominator straight s subscript 1 end fraction end style over denominator begin display style bevelled straight d subscript 2 over straight s subscript 2 end style end fraction as space the space distance space covered space in space both space cases space is space the space same comma space straight d subscript 1 space and space straight d subscript 2 space get space nullified. The space ratio space of space time space straight t subscript 1 space and space straight t subscript 2 space will space be fraction numerator space straight t subscript 1 over denominator space straight t subscript 2 end fraction equals fraction numerator begin display style bevelled fraction numerator space 1 over denominator straight s subscript 1 end fraction end style over denominator begin display style bevelled 1 over straight s subscript 2 end style end fraction fraction numerator space straight t subscript 1 over denominator space straight t subscript 2 end fraction equals straight s subscript 2 over straight s subscript 1 end style
Now speed s1 is the speed of boat when upstream, i.e the difference of speed of boat in still water and the speed of water
s1 =u-v m/s and 
s2 is the speed of boat when downstream, i.e the sum of speed of boat in still water and the speed of water
s2=u+v m/s
Therefore, the ratio of t1 and t2 is s2 i.e u+v by S1 i.e u-v.
Answered by Abhijeet Mishra | 17 Aug, 2018, 12:53: PM

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