A ,man wishing to cross a river flowing with velocity `u` jumps at an angle `theta` with the river flow.
(a) Find the net velocity of the man with respect to ground if he can swim with speed `v` in still water.
(b) In what direction does the boat actually move ?
( c) Find how far from the point directly opposite to the starting point does the boat reach the opposite bank, if the width of the river is `d`.

Explanation

(a) `v_(M R) = v, v_R = u`
`vec v_M = vec v_(M R) + vec v_R`
Therefore, velocity of man,
`v_M = sqrt(u^2 + v^2 + 2 v u cos theta)`
(b) `tan phi = (v sin theta)/(u + v cos theta)`
( c) `(v sin theta) t = d rArr t = (d)/(v sin theta)`
`x = (u + v cos theta) (d)/(v sin theta)`.
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