A man wants to reach point `B` on the opposite bank of a river flowing at a speed `u` as shown in (Fig. 5.193). What minimum speed relative to water to water should the man have so that he can reach directly to point `B` ? In which direction should he swim ?
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Answer

`(u)/(sqrt(2)), 45^@` with upstream.

Explanation

`vec v_m = vec v_(m//w) + vec v_w = v cos(theta + 45^@) hat i + v sin (theta + 45^@) hat j`
`+ u cos 45^@ hat i - u sin 45d hat j = [v cos(theta + 45^@)+ u cos 45^@]hat i`
`+[v sin(theta + 45^2 - u sin 45^@] hat j`
To reach the point `B`, `hat j` component should be zero
`v sin (theta + 45^@) = u sin 45^@`
`rArr v = (u sin 45^@)/(sin(theta + 45^@))`
For `v_(min), theta + 45^@ = 90^@ rArr theta = 45^@`
`rArr v_(min) = (u)/(sqrt(2)), 45^@` with upstream.
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