Grade 12th passMechanics

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]

Question image for To cross the river in shortest distance, a swimme

ANGT

8 Years agoGrade 12th pass

4 Answers

Eshan

8 Years ago

Praveen

7 Years ago

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

Tejaswi

6 Years ago

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

Kushagra Madhukar

5 Years ago

Dear student,

Please find the solution to your problem.

Let the velocity of river be v_r and velocity of swimmer be v_sr

For the shortest time case-

Time taken to cross river, t₁ = d/v_sr

For shortest distance case-

Time taken to cross river, t₂ = d/v_srcosθ

where θ is the angle made by swimmer w.r.t the direction normal to the direction of flow of river.

where cosθ = (v_sr² – v_r²)^1/2/v_sr

Hence, t₁/t₂ = cosθ = √(1 – (v_r/v_sr)²)

Thanks and regards,

Kushagra

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ANGT

4 Answers

Eshan

Praveen

Tejaswi

Kushagra Madhukar

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