Crossing the River (Minimum Distance)

Q. A boat which has a speed of 5 km/h in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/h is:

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

Q.

How long after the beginning of motion is the displacement of a harmonically oscillating point equal to one half its amplitude, if the period is 24 sec and initial phase is zero?

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. displacement time equation of a particle executing SHM is, x=sin[(π/3)t+π/6]cm. The distance of a particle in 3 seconds is

Q. The stream of a river is flowing with a speed of $2\text{km/h}$. A swimmer can swim at a speed of $4\text{km/h}$. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight ?

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

Q. A swimmer wishes to cross a $500m$ wide river flowing at $5Km/h$. His speed with respect to water is $3Km/h$.
Find the shortest possible time to cross the river.

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 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 man can swim at a speed 2 m/s in still water. He starts swimming in a river at an angle 150 to the direction of water flow and reaches the directly the directly opposite point on the opposite bank.
(a) Find the speed of flowing water.
(b) If width od river is 1 km then calculate the time taken to cross the river.

Q.

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

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. 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 swimmer can swim in still water with a speed of .$\sqrt{5}$ m/s. While crossing a river his average speed is 3 m/s. If he cross the river in the shortest possible time, what is the speed of flow of water?

1. 6 m/s
2. 2 m/s
3. 8 m/s
4. 4 m/s

Q.

A swimmer wants to cross a 200m wide river which is flowing at a speed of 2m/s. The velocity of the swimmer with respect to river is 1m/s. How far from the point directly opposite to the straight point does the swimmer reach the opposite bank?

Q. A man crosses a river in a boat. If he crosses the river in minimum time he takes 10 minutes with a drift 120m. If he crosses the river taking shortest path, he takes 12.5 minute, find
(i) width of the river, (ii) velocity of the boat with respect to water, (iii) speed of the current.
Assume $v_{b/r}>v_r$

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 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 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 swimmer wants to cross a $200m$ wide river which is flowing at a speed of $2m/s$. The velocity of the swimmer with respect to river is $1m/s$. How far from the point directly opposite to the starting point does the swimmer reach the opposite bank?

1. $200m$
2. $600m$
3. $800m$
4. $400m$

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.

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. Sin ( $\frac{3}{5}$ )

2. $co{s}^{-1}\left(\frac{3}{5}\right)$

3. $ta{n}^{-1}\left(\frac{3}{5}\right)$

4. $si{n}^{-1}\left(\frac{3}{5}\right)$

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

Q. The rowing speed of a man relative to water is $5$ $km/h$ and the speed of water flow is $3$ $km/h$. At what angle to the river flow should he head if he wants to reach a point on the other bank, directly opposite to starting point?

1. ${127}^0$
2. ${143}^0$
3. ${120}^0$
4. ${150}^0$