Question

A swimmer should swim making an angle theta with the upstream meaning

Answer 1

✌❤HEYA_MATE❤✌

Taking d to be the width of the river and also the the shortest distance covered by the swimmer.

If the swimmer makes an angle θ with the upstream, then angle (90-θ) will be normal to the stream.

Thus, shortest time taken will be the own distance i.e t=d/v.

If speed of the river is v.

Thus, making an angle (90-θ) will be cos(90-θ)  and so speed will be vcos(90-θ).

The shortest distance to cover the river in time will be

t1 = d/vcos(90-θ)

t1= d/vsin(θ).

The ratio will be  t/t1

              =(d/v)/(d/vsin(θ))

              = sinθ.

✌❤PIYUSH_SHARMA❤✌

Answer 2

☆$\red {HELLO\:DEAR}$☆

Taking d to be the width of the river and also the the shortest distance covered by the swimmer.

If the swimmer makes an angle θ with the upstream, then angle (90-θ) will be normal to the stream.

Thus, shortest time taken will be the own distance i.e t=d/v.

If speed of the river is v.

Thus, making an angle (90-θ) will be cos(90-θ)  and so speed will be vcos(90-θ).

The shortest distance to cover the river in time will be

t1 = d/vcos(90-θ)

t1= d/vsin(θ).

The ratio will be  t/t1

              =(d/v)/(d/vsin(θ))

              = sinθ.

☆$\green {VISHU\:PANDAT}$☆

☆$\blue {FOLLOW\:ME}$☆