Q. No.A river of width \(200~\text{m}\) flows from west to east with a speed of \(18~\text{km/h}.\) A boat moves with a speed of \(36~\text{km/h}\) in still water. If the boat makes a round trip from one bank to the opposite bank and back, what are the minimum time taken for the journey and the net displacement along the river bank, respectively?
1. \(20~\text{s}~\text{and}~100~\text{m}~\)
2. \(40~\text{s}~\text{and}~0~\text{m}~\)
3. \(40~\text{s}~\text{and}~200~\text{m}~\)
4. \(40~\text{s}~\text{and}~100~\text{m}~\)
1. \(20~\text{s}~\text{and}~100~\text{m}~\)
2. \(40~\text{s}~\text{and}~0~\text{m}~\)
3. \(40~\text{s}~\text{and}~200~\text{m}~\)
4. \(40~\text{s}~\text{and}~100~\text{m}~\)
Subtopic: Relative Motion |
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A river is flowing from west to east direction with speed of \(9 ~\text{kmh}^{-1}.\) If a boat capable of moving at a maximum speed of \(27 ~\text{kmh}^{-1} \) in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \(150^\circ\) to direction of river flow, then the width of the river is:
1. \(300 ~\text m\)
2. \(75 ~\text m\)
3. \(112.5 ~\text m\)
4. \(112.5\sqrt3 ~\text m \)
1. \(300 ~\text m\)
2. \(75 ~\text m\)
3. \(112.5 ~\text m\)
4. \(112.5\sqrt3 ~\text m \)
Subtopic: Relative Motion |
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The maximum speed of a boat in still water is \(27~\text{km/h.} \) Now this boat is moving downstream in a river flowing at \(9~\text{km/h.} \) A man in the boat throws a ball vertically upwards with speed of \(10~\text{m/s} \). Range of the ball as observed by an observer at rest on the river bank, is: (in m) Take \(g=10~ \text{m/s}^2 \))
1. \(20\)
2. \(200\)
3. \(2000\)
4. \(1000\)
1. \(20\)
2. \(200\)
3. \(2000\)
4. \(1000\)
Subtopic: Relative Motion |
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Two trains are moving on parallel north–south tracks. Train \(A\) is travelling northward, \(72~\text{km/hr},\) while train \(B\) is travelling southward at \(108~\text{km/hr}.\) What is the velocity of the train \(B\) with respect to train \(A\)?
1. \(36~\text{km/hr}\) south
2. \(36~\text{km/hr}\) north
3. \(180~\text{km/hr}\) south
4. \(180~\text{km/hr}\) north
1. \(36~\text{km/hr}\) south
2. \(36~\text{km/hr}\) north
3. \(180~\text{km/hr}\) south
4. \(180~\text{km/hr}\) north
Subtopic: Relative Motion |
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A swimmer swims perpendicular to river flow and reaches point \(B\). If the velocity of the swimmer in still water is \(4\) km/hr, the velocity of the river flow is:
| 1. | \(3\) km/hr | 2. | \(5\) km/hr |
| 3. | \(2\) km/hr | 4. | \(6\) km/hr |
Subtopic: Relative Motion |
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A girl standing on the road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without an umbrella with a speed of \(15 \sqrt{2}~\text{km/h}, \) the raindrops hit her head vertically. The speed of raindrops with respect to the moving girl is:
1. \(30~\text{km/h} \)
2. \(\dfrac{25}{\sqrt{2}}~\text{km/h}\)
3. \(\dfrac{30}{\sqrt{2}}~\text{km/h}\)
4. \(25~\text{km/h} \)
1. \(30~\text{km/h} \)
2. \(\dfrac{25}{\sqrt{2}}~\text{km/h}\)
3. \(\dfrac{30}{\sqrt{2}}~\text{km/h}\)
4. \(25~\text{km/h} \)
Subtopic: Relative Motion |
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A swimmer wishes to cross a river from a point \(A\) to a point \(B.\) The line \(AB\) makes an angle of \(30^\circ\) with the direction of the river flow. If the swimmer’s speed relative to water is equal to the speed of the river current, at what angle \(\theta\) with respect to the line \(AB\) should the swimmer swim so that he reaches the point \(B\text{?}\)
| 1. | \(30^\circ\) | 2. | \(45^\circ\) |
| 3. | \(60^\circ\) | 4. | \(90^\circ\) |
Subtopic: Relative Motion |
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A person is swimming at a speed of \(10~\text{m/s}\) at an angle of \(120^\circ\) with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is:
1. \(3~\text{m/s}\)
2. \(5~\text{m/s}\)
3. \(7~\text{m/s}\)
4. \(9~\text{m/s}\)
1. \(3~\text{m/s}\)
2. \(5~\text{m/s}\)
3. \(7~\text{m/s}\)
4. \(9~\text{m/s}\)
Subtopic: Relative Motion |
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A swimmer can swim at \(12~\text{km/h}\) relative to still water. A river flows at \(6~\text{km/h}.\) along its length. To reach the point directly opposite the starting point on the other bank, at what angle should the swimmer head with respect to the direction of river flow?
1. \(160^\circ\)
2. \(140^\circ\)
3. \(120^\circ\)
4. \(150^\circ\)
Subtopic: Relative Motion |
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A particle is moving along the \(x\text-\)axis with its coordinate with time ‘\(t\)’ given by \(x(t) = 10 +8t-3t^2. \) Another particle is moving along the \(y\text-\)axis with its coordinate a function of time given by \(y(t) = 5-8t^3. \) At \(t = 1 ~\text s, \) the speed of the second particle as measured in the frame of the first particle is given as \(\sqrt{v}~\text{m/s}, \) the value of \(v\) is:
| 1. | \(580\) | 2. | \(350\) |
| 3. | \(230\) | 4. | \(110\) |
Subtopic: Relative Motion |
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