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A motion boat going down stream comes over a floating body at a point A. 60 minutes later it turned back and after some time passed the floating body at a distance of 12km from the point A. Find the velocity  of the stream assuming constant velocity for the motor boat in still water

Asked by valavanvino1011 31st August 2018, 6:54 AM
Answered by Expert
Answer:
Let speed of stream U km/hr and speed of motion boat in still water be V km/hr.
 
down strem speed of motion boat = (U+V) km/hr
 
distance moved by motion boat while travelling downstream after crossing point A = (U+V)×1 = (U+V) km ..................(1)
 
let t be time in hour for the motor boat to meet the floating object after it has turned back. 
 
Hence in (1+t) hour floating object has travelled 12 km, hence we have, 12 = U×(1+t) ..................(2)
 
The time t is written as , using the upstream speed (V-U) of motion boat and
the distance [(U+V)-12 ] km travelled for its backward journey.
 
t = [(U+V)-12 ] / (V-U) ......................(3)
 
By substituing t from (3) in (2), we get,    begin mathsize 12px style 12 space equals space U cross times open parentheses 1 plus fraction numerator V plus U minus 12 over denominator V minus U end fraction close parentheses space equals space U cross times open parentheses fraction numerator 2 cross times V minus 12 over denominator V minus U end fraction close parentheses space end style .......................(4)
begin mathsize 12px style 12 V space minus space 12 U space equals space 2 cross times V cross times U space minus space 12 U space space
12 V space equals space 2 cross times V cross times U space o r space U space equals space 6 space k m divided by h r end style

Answered by Expert 31st August 2018, 12:08 PM
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