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 man wishes to cross a river in a boat. If he crosses the river in minimum time, he takes $10$ minutes with a drift of $120m$. If he crosses the river taking shortest route, he takes $12.5$ minutes, find the velocity of the boat with respect to water.

1. $20m/min$
2. $12m/min$
3. $10m/min$
4. $8m/min$

Q. A river is flowing from west to east at a speed of $5\text{m/min}$. A man on the south bank of the river, capable of swimming at $10\text{m/min}$ in still water, wants to swim across the river in the shortest time. He should swim in a direction

1. due north
2. ${30}^{\circ }$ east of north
3. ${30}^{\circ }$ west of north
4. ${60}^{\circ }$ east of north

Q. A river is flowing from west to east at a speed of $5\text{m/min}$. A man on the south bank of the river, capable of swimming at $10\text{m/min}$ in still water, wants to swim across the river in the shortest time. He should swim in a direction

1. due north
2. ${30}^{\circ }$ east of north
3. ${30}^{\circ }$ west of north
4. ${60}^{\circ }$ east of north

Q.

A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point ‘C’ starting from ‘A’. He swims with a speed of 5 km/hr at an angle $\theta$ w.r.t the river flow. If AB =BC =400 m, what is the value of $\theta$?

1. ${37}^{\circ }$

2. ${53}^{\circ }$

3. ${30}^{\circ }$

4. ${60}^{\circ }$

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 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 is flowing with a speed of 1 km/hr. A swimmer wants to go to point ‘C’ starting from ‘A’. He swims with a speed of 5 km/hr at an angle $\theta$ w.r.t the river flow. If AB =BC =400 m, what is the value of $\theta$?

1. ${37}^{\circ }$

2. ${53}^{\circ }$

3. ${30}^{\circ }$

4. ${60}^{\circ }$

Q. A man wishes to cross a river in a boat. If he crosses the river in minimum time, he takes $10$ minutes with a drift of $120m$. If he crosses the river taking shortest route, he takes $12.5$ minutes, find the velocity of the boat with respect to water.

1. $20m/min$
2. $12m/min$
3. $10m/min$
4. $8m/min$