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NEET Class neet Answered

a boat having a speed of 5km/hr . in still water crossing a river of width 1km long the shortest possible paths in 15 min the speed of the river in km/ hr
Asked by kishorantarkar26 | 05 Sep, 2023, 02:58: AM
answered-by-expert Expert Answer
Vector diagram showing velocity of boat and velocity of river are shown above.
 
u is velocity of boat so that direction of velocit of boat u makes angle θ with the line parallel to width of river.
 
ur is velocity of river.
 
magnitude of velocity of boat , u = 5 km / hr =  5 × ( 5 / 18) m/s = ( 25/18 ) m/s
 
velocity component along the line parallel to width of river = u cosθ .
 
If boat travels along shortest path to cross the river  and time taken to cross the river is 15 min ,
 
then we have
 
begin mathsize 14px style u space cos theta space cross times space 15 space cross times space 60 space equals space 1000 space m end style
 
If we substitute u = ( 25/18 ) m/s , then we get
 
begin mathsize 14px style 25 over 18 cross times space cos theta cross times 900 space equals space 1000 space m end style
 
From above expression we get , cosθ = 0.8
 
Hence , sinθ = begin mathsize 14px style square root of 1 space minus space left parenthesis 0.8 right parenthesis squared end root space equals space 0.6 end style
From vector diagram, we see that
 
begin mathsize 14px style u subscript r subscript space end subscript space equals space u space sin theta space equals space 25 over 18 cross times 0.6 space m divided by s space equals space 5 over 6 space m divided by s end style
Hence, speed of river = (5/6) × (18/5) km/hr = 3 km/hr
Answered by Thiyagarajan K | 05 Sep, 2023, 01:21: PM
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