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A man wants to reach point B on the oppo...

A man wants to reach point B on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point B? In which direction should he swim?

Text Solution

Verified by Experts

The correct Answer is:
B
Let v be the speed of boatman in still water.

Resultant of v and u should be along AB. Components of `v_b` (absolute velocity of boatman ) along
x and y -direction are,
`v_x=u-vsin theta`
and `v_y=vcos theta`
Further, `tan 45^@=(v_y)/(v_x)`
or `1=(vcos theta)/(u-vsin theta)`
`:. v=u/(sin theta+cos theta)`
`=u/(sqrt2 sin(theta+45^@))`
v is minimum at, `theta+45^@=90^@`
or `theta=45^@`
and `v_(min)=u/sqrt2`
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