Question

Question #48714

To cross the river in shortest distance, a swimmer should swim making an angle '0' with the upstream. What is the ratio of 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 speed of river.}
(1) cos '0'
(2)sin'0'
(3)tan'0'
(4)cot'0'

Expert's answer

Answer on Question #48714, Physics, Other

Task:

To cross the river in shortest distance, a swimmer should swim making an angle '0' with the upstream. What is the ratio of 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 speed of river.}

(1) cos '0'

(2) sin'0'

(3) tan'0'

(4) cot'0'

Solution:

So if speed of swimmer in still water is greater than speed of river, we neglect speed of the river.

the ratio of time taken to swim across in the shortest time to that in swimming across over shortest distance $t = V\cos'0'/V\sin'0' = \cot'0'$ .

Answer: (4)cot'0'.

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Comments

Assignment Expert

04.06.18, 16:14

Dear visitor, please use panel for submitting new questions

Sahil agrawal

03.06.18, 10:03

The minimum time taken is when cos theta is 0 which is d/v... When the swimmer starts with a velocity perpendicular to that of the velocity of river. And as shown above the time taken to cover minimum distance is d/vsin0. So the ratio is d/v/d/vsin0 which is sin0