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Grade: 12th pass

                        

To cross the river in shortest distance, a swimmer should swim making angle theta with the upstream. What is the ratio of the time taken to swim across in the shortest time to that in swimming across over shortest distance. [Assume speed of swimmer in still water is greater than the speed of river flow]

2 years ago

Answers : (4)

Eshan
askIITians Faculty
2095 Points
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2 years ago
Praveen
13 Points
							
t(shortest)=t1=d/v(sr)
t(shortest distance)=t2=d/v(sr)sin(theta)
=t1/t2= sin (theta)
Where d is width of river
one year ago
Tejaswi
15 Points
							
Answer is sin (theta)
 
As t shortest=t¹=d/v(sr)
T(shortest)=t²=d/v(sr) sin (theta)
=t¹/t²=sin (theta)
Where d is width of river
 
one year ago
Kushagra Madhukar
askIITians Faculty
605 Points
							
Dear student,
Please find the solution to your problem.
 
Let the velocity of river be vr and velocity of swimmer be vsr
 
For the shortest time case-
Time taken to cross river, t1 = d/vsr
 
For shortest distance case-
Time taken to cross river, t2 = d/vsrcosθ
where θ is the angle made by swimmer w.r.t the direction normal to the direction of flow of river.
where cosθ = (vsr2 – vr2)1/2 /vsr
 
Hence, t1/t2 = cosθ = √(1 – (vr/vsr)2)
 
Thanks and regards,
Kushagra
 
4 months ago
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