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![[Post New]](/templates/default/images/icon_minipost_new.gif) 12 May 2007 16:33:11 IST
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A steam boat goes across a lake and comes back (1)On a quiet and calm day when the water is still (2)On a rough day when there is a uniform current so as to help the journey onwards and to impede the journey backwards. With the same speed of launch on both days the times taken to complete the two-way journey on the quiet and rough day are t1 and t2. THEN 1) t1 < t2 2) t1=t2 3) t1>t2 4) t1>_<t2 plz give answer by solving and expanation
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12 May 2007 16:39:20 IST
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is the ans. 2 option: t1=t2????
on frst day, time taken = t+t=2t
on second day, time taken = t+delta t + t - delta t
delta t is added and removed time due to help in motion by current
t2=2t
therefore t1=t2....
plzz rate if correct and guide if wrong....
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12 May 2007 16:40:04 IST
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correct answer shouid be 3
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12 May 2007 16:46:35 IST
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bcoz
let velocity of boat =V
let velocity of water=U
velocity in still water=V
velocity on rough day=V-U
let it cover distance d
ON ROUGH DAY
during upsteam time taken T3=d/V-U
during downsteam time taken T4=d/V+U
total time t1 =T3+T4=2Vd/V2-U2........1
IN STILL WATER
total distance =2d so total time t2 =2d/V................2
subtract 1 from 2 u will get
t2-t1=2d/V *(1-1/1-U2-V2) here V2= square of V U2= square of U
this is always + quantity hence t1>t2
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12 May 2007 16:47:38 IST
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good job yaar,,,but the answer given in the book is 1) t1<t2.....i dont know how..plz help
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12 May 2007 16:49:55 IST
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time taken in still water shouid be greater then in running water is it not?
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12 May 2007 16:53:44 IST
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in ur earlier solution ..army..u hav missed d in 1..
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12 May 2007 17:01:07 IST
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but tht was just typing mistake yaar plz see again answer shouid be TIME TAKEN IN STILL WATER IS > TIME TAKEN WHEN WATER IS FLOWING
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12 May 2007 17:05:03 IST
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oops is it ACROSS the river then the answer will be 1 but only if the boat return to same place from where it had started its journey so answer will be 1 t1<t2
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12 May 2007 17:07:52 IST
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but if the boat goes along the river then answer will be 3 
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12 May 2007 17:08:10 IST
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the answer given is t1<t2
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12 May 2007 17:10:21 IST
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ya it is across the river ,,then why 1
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12 May 2007 17:11:18 IST
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bcoz during rough day u have to make some angle with the flow of river so that the resultant velocity of boat and flow of river become perpendicular to the flow and u may reach on just opposite
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12 May 2007 17:11:46 IST
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let me give u whole equations
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12 May 2007 17:13:46 IST
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ok
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