A river is flowing from S to N at a speed of $5 m$ ${m i n}^{- 1}$ . A man on the west bank of the river capable of swimming at $10 m$ ${m i n}^{- 1}$ in still water wants to swim across the river in the shortest time. In what direction should he swim?

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Solution

R.E.F image
if the travell due east then his Resultant
Velocity (due to velocity of down strem of
water) acts 30 east of south and the
distance to be covered to reach the
other bank increased to $= x / c o s 30$
i.e. resultant velocity is 11.2 m/min.
So time taken is $\frac{x}{9.7} m i n$ .
So he must travel to due east.

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A river is flowing from S to N at a speed of 5m min−1. A man on the west bank of the river capable of swimming at 10m min−1 in still water wants to swim across the river in the shortest time. In what direction should he swim?

R.E.F imageif the travell due east then his Resultant Velocity (due to velocity of down strem of water) acts 30 east of south and the distance to be covered to reach the other bank increased to =x/cos30i.e. resultant velocity is 11.2 m/min.So time taken is x9.7min.So he must travel to due east.

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