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

1. Due north
2. Due north-east
3. Due north-east with double the speed of the river
4. None of the above

Subtopic:  Relative Motion |
 59%
From NCERT
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A thief is running away on a straight road in a jeep moving with a speed of 9 m/s. A police man chases him on a motor cycle moving at a speed of 10 m/s. If the instantaneous separation of jeep from the motor cycle is 100 m, how long will it take for the policemen to catch the thief

(1) 1 second

(2) 19 second

(3) 90 second

(4) 100 second

Subtopic:  Relative Motion |
 85%
From NCERT
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A man sitting in a bus travelling in a direction from west to east with a speed of \(40\) km/h observes that the rain-drops are falling vertically downwards. To another man standing on ground the rain will appear: 

1. To fall vertically downwards
2. To fall at an angle going from west to east
3. To fall at an angle going from east to west
4. The information given is insufficient to decide the direction of the rain
Subtopic:  Relative Motion |
 53%
From NCERT
PMT - 1999
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A boat takes two hours to travel 8 km and back in still water. If the velocity of water is 4 km/h, the time taken for going upstream 8 km and coming back is 

(1) 2h

(2) 2h 40 min

(3) 1h 20 min

(4) Cannot be estimated with the information given

Subtopic:  Relative Motion |
 65%
From NCERT
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A 120 m long train is moving towards west with a speed of 10 m/s. A bird flying towards east with a speed of 5 m/s crosses the train. The time taken by the bird to cross the train will be 

(1) 16 sec

(2) 12 sec

(3) 10 sec

(4) 8 sec

Subtopic:  Relative Motion |
 85%
From NCERT
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A boat crosses a river with a velocity of 8 km/h. If the resulting velocity of boat is 10 km/h, then the velocity of river water is 

(1) 4 km/h

(2) 6 km/h

(3) 8 km/h

(4) 10 km/h

Subtopic:  Relative Motion |
 89%
From NCERT
PMT - 2001
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A vector \(\vec{a}\) is turned without a change in its length through a small angle \(d\theta\). The values of \(\left | \Delta \vec{a} \right |\) and \(\Delta a\) are respectively:
1. \(0,\)  \(ad\theta\)
2. \(ad\theta,\) \(0\)
3. \(0,\) \(0\)
4. none of these

Subtopic:  Position & Displacement |
 55%
From NCERT
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A steam boat goes across a lake and comes back (a) On a quiet day when the water is still and (b) On a rough day when there is a uniform air current so as to help the journey onward and to impede the journey back. If the speed of the launch on both the days was the same, in which case will the steam boat complete the journey in lesser time:

1. Case (a)
2. Case (b)
3. Same in both case
4. Nothing can be predicted based on given data
Subtopic:  Relative Motion |
From NCERT
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To a person, going eastward in a car with a velocity of 25 km/hr, a train appears to move towards north with a velocity of 253 km/hr. The actual velocity of the train will be

(1) 25 km/hr

(2) 50 km/hr

(3) 5 km/hr

(4) 53 km/hr

Subtopic:  Relative Motion |
 78%
From NCERT
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Two particles having position vectors \(\overrightarrow{r_{1}} = \left( 3 \hat{i} + 5 \hat{j}\right)\) metres and \(\overrightarrow{r_{2}} = \left(- 5 \hat{i} - 3 \hat{j} \right)\) metres are moving with velocities \(\overrightarrow{v}_{1} = \left( 4 \hat{i} + 3 \hat{j}\right)\)\(\text{m/s}\) and \(\overrightarrow{v}_{2} = \left(\alpha\hat{i} + 7 \hat{j} \right)\)\(\text{m/s}\). If they collide after \(2\) seconds, the value of \(\alpha\) is:

1. \(2\) 2. \(4\)
3. \(6\) 4. \(8\)
Subtopic:  Relative Motion |
 51%
From NCERT
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