Crossing the River (Minimum Distance)

Q.

River is flowing at 3 Km/h in the west direction and You can swim at a maximum speed of 5 Km/h , then at what direction must you swim so that you end up swimming perpendicular to the bank?

1. tan^-1(⅗)

2. sin^-1(⅗)

3. sin(⅗)

4. cos^-1(⅗)

Q.

River is flowing at 3 Km/h in the west direction and You can swim at a maximum speed of 5 Km/h , Given if the river is 12 km wide, How long will you take to cross the river?

1. 4 hr

2. 2.4 hr

3. 3 hr

4. Data insufficient

Q. A man wishes to cross a river and come back to original position by swimming minimum distance. If the width of the river is 50 m, speed of river is 2 m/s and velocity of man with respect to river is 4 m/s, then time taken by man to come back to original position is

1. 
   $\frac{50}{\sqrt{3}}$ sec
2. 
   50$\sqrt{2}$ sec
3. 
   25 sec
4. 
   25$\sqrt{3}$ sec

Q. A boat moves relative to water with a velocity $u$ and river is flowing with $2u$. At what angle with the stream should the boat move to have minimum drift ?

1. ${60}^{\circ }$
2. ${90}^{\circ }$
3. ${120}^{\circ }$
4. ${30}^{\circ }$

Q. A boat which has a speed of $5\text{km/h}$ in still water crosses a river of width $1\text{km}$ along the shortest possible path in $15\text{min}$. The velocity of the river water in $\text{km/h}$ is

1. $1$
2. $3$
3. $4$
4. $\sqrt{41}$

Q. A swimmer can swim in still water with a speed of 3 km/hr. Rate of flow of river is 6 km/hr. If the swimmer swims at angle ${60}^o$ with flow of river, find speed of swimmer as seen by person, who is moving in a boat in the river.

1. 7 km/hr
2. 9 km/hr
3. 3 km/hr
4. 2 km/hr

Q. A man can swim with a speed of 4.0 km/h in still water. How long does he take tocross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes hisstrokes normal to the river current? How far down the river does he go when he reaches the other bank ?

Q. A boat which has a speed of $5\text{km/h}$ in still water crosses a river of width $1\text{km}$ along the shortest possible path in $15\text{min}$. The velocity of the river water in $\text{km/h}$ is

1. $1$
2. $3$
3. $4$
4. $\sqrt{41}$

Q.

River is flowing at 3 Km/h in the west direction and You can swim at a maximum speed of 5 Km/h , Given if the river is 12 km wide, How long will you take to cross the river?

1. 4 hr

2. 2.4 hr

3. 3 hr

4. Data insufficient

Q. A man wishes to cross a river and come back to original position by swimming minimum distance. If the width of the river is 50 m, speed of river is 2 m/s and velocity of man with respect to river is 4 m/s, then time taken by man to come back to original position is

1. 
   $\frac{50}{\sqrt{3}}$ sec
2. 
   50$\sqrt{2}$ sec
3. 
   25 sec
4. 
   25$\sqrt{3}$ sec