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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 in Fig. What minimum speed relative to water should the man have so that he can reach directly to point B? In which direction should be swim?
985228_09c7aa443f124501a3265072a22f45d5.png

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Solution

¯vm=¯vm/w+¯vw
=vcos(θ+45o)^i+vsin(θ+45o)^j+ucos45o^iu sin45o^j

=[vcos(θ+45o)+ucos45o]^i+[vsin(θ+45ousin45o]^j
to reach the point B ^j component should be zero
vsin(θ+45o)=usin45o

v=usin45osin(θ+45o)

For vmin,θ+45o=90oθ=45o

vmin=u2,45o with upstream

1031654_985228_ans_97417d38d9ab4c3b957e4a88cc0dad79.png

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