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Question

A man wants to reach point B on the opposite bank of a river flowing at a speed u as shown. What minimum velocity relative to water should the man have so that he can reach directly to point B?


A
u2, in the upstream at an angle 45 with the vertical
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B
2u, in the upstream at an angle 45 with the vertical
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C
u2, in the downstream at an angle 45 with the vertical
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D
2u, in the downstream at an angle 45 with the vertical
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Solution

The correct option is A u2, in the upstream at an angle 45 with the vertical
Let v be the velocity of man w.r.t flow in a direction at an angle θ with the direction perpendicular to flow.
For the man to go along AB,
Along y-axis, vsin(θ+45)=usin45
for him to go along AB, then
v=usin45sin(θ+45)
For v to be minimum, sin(θ+45) should be maximum
θ+45=90
θ=45
Vmin=u2, in the upstream at an angle 45 to the vertical.

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