The path of a projectile in the absence of air drag is shown in the figure by dotted line. If the air resistance is not ignored , then which one of the paths shown in the figure is appropriate for the projectile ?

1. B

2. A

3. D

4. C

A man standing on a road holds his umbrella at 30° with the vertical to keep the rain away. He throws the umbrella and starts running at 10 km/hr. He finds that raindrops are hitting his head vertically, the speed of raindrops with respect to the road will be:

1. 10 km/hr

2. 20 km/hr

3. 30 km/hr

4. 40 km/hr

A boat is moving with a velocity \(3\hat i + 4\hat j\) with respect to ground. The water in the river is moving with a velocity\(-3\hat i - 4 \hat j\) with respect to ground. The relative velocity of the boat with respect to water is: 
1. \(8\hat j\)
2. \(-6\hat i-8\hat j\)
3. \(6\hat i+8\hat j\)
4. \(5\sqrt{2}\)

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:

A person, aiming to reach the exact opposite point on the other bank of a stream, is swimming with a speed of \(0.5\ \text{m/s}\) at an angle of \(120^\circ\) to the direction of the flow of water. The speed of water in the stream is:

1. \(1\ \text{m/s}\)

2. \(0.5\ \text{m/s}\)

3. \(0.25\ \text{m/s}\)

4. \(0.433\ \text{m/s}\)

A thief is running away on a straight road in a jeep moving with a speed of \(9\ \text{m/s}\). A police man chases him on a motorcycle moving at a speed of \(10\ \text{m/s}\). If the instantaneous separation of the jeep from the motorcycle is \(100\ \text{m}\), how long will it take for the policeman to catch the thief:

1. \(1\) second

2. \(19\) second

3. \(90\) second

4. \(100\) second

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: 

A boat takes two hours to travel \(8\ \text{km}\) and back in still water. If the velocity of water is \(4\ \text{km/h}\), the time taken for going upstream \(8\ \text{km}\) and coming back is:

1. \(2\ \text{h}\)

2. \(2\ \text{h}\ 40\ \text{min}\)

3. \(1\ \text{h}\ 20\ \text{min}\)

4. Cannot be estimated with the information given

A \(120\ \text{m}\) long train is moving towards west with a speed of \(10\ \text{m/s}\). A bird flying towards east with a speed of \(5\ \text{m/s}\) crosses the train. The time taken by the bird to cross the train will be:

1. \(16\ \text{s}\)

2. \(12\ \text{s}\)

3.  \(10\ \text{s}\)

4. \(8\ \text{s}\)

A boat crosses a river with a velocity of \(8\ \text{km/h}\). If the resulting velocity of the boat is \(10\ \text{km/h}\), then the velocity of the river water is:

1. \(4\ \text{km/h}\)

2. \(6\ \text{km/h}\)

3. \(8\ \text{km/h}\)

4. \(10\ \text{km/h}\)