Q. A person while swimming crosses a 200 m wide river in a minimum time 40 seconds and when he crosses the river straight to opposite bank he took 50 seconds. A)The speed of the man is 5m/s. B)The...

Q. A person while swimming crosses a 200 m wide river in a minimum time 40 seconds and when he crosses the river straight to opposite bank he took 50 seconds.

A)The speed of the man is 5m/s.

B)The speed of the river water is 3 m/s.

C)The horizontal drift of the man while crossing the river in 40 s is 160 m.

D)The speed of the man is 4m/s.

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Let the river run from West to East with parallel sides 200m apart. Let the swimmer begin at A and end at B. Note that B is some distance downstream from A due to the current. Then let the swimmer cross to C perpendicular from B.

The swimmers speed is 5m/s as all effort from A to B is expended perpendicular to the bank. (It is the least time.) Since he crosses 200m in 40 sec he travels at 5m/s.

When crossing from B to C he must aim at an angle `theta` upstream. Thus his forward progress is `5costheta` (cosine of `/_ABC` ). Since we know his time from B to C we know that `5costheta=4 ==> costheta=4/5` or `theta~~36.9^@` .

Since `costheta=4/5` we find that ``AB=250m and AC=150m.

The current's speed can be found since the swimmer went downstream 150m in 40 sec so the current is 3.75m/s.

Check: the trip from A to B has 2 components: 5m/s directly across the river and 3.75m/s downstream with a resultant 6.25m/s. The distance from A to B is 250m, covered in 40 sec which is a resultant speed of 6.25m/s.

So A is correct.

B is incorrect -- the current is 3.75m/s

C is incorrect as the horizontal drift is 150m

D is incorrect as A is correct.

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The correct answer is A

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