Crossing the River(Minimum Time)

Q. A man is capable of swimming at $10\text{m/s}$ in still water. If he has to cross a river flowing at $5\text{m/s}$ and reach the opposite shore in the least possible time, how far along the river will he drift if distance between the two shore is $100\text{m}$.

1. $5\text{m}$
2. $10\text{m}$
3. $50\text{m}$
4. $100\text{m}$

Q. A river $5\sqrt{3}km$ wide flows with a velocity of $5kmph$. A boat which can move with a velocity of $10kmph$ in still water crosses the river, without any drift. For this, the boat has to tilt its velocity by $\theta$ with the straight path in the right direction (see figiure). If the boat's velocity is tilted by the same angle $\theta$ in the wrong direction, the drift will be

1. $8.1km$
2. $9.1km$
3. $10km$
4. $12km$

Q. A man wants to cross the river to an exactly opposite point on the other bank. If he can row his boat with $\frac{2}{\sqrt{3}}$ times the velocity of the current, then at what angle to the current he must keep the boat pointed ?

1. ${120}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${150}^{\circ }$

Q. A man can row a boat at $4km/h$ in still water. What is the minimum possible time in which he can cross the river if the speed of the current is $4km/h$ and the width of the river is $8km$?

1. $1h$
2. $2h$
3. $\sqrt{3}h$
4. $\sqrt{2}h$