The horizontal range of a projectile is \(4 \sqrt{3}\) times its maximum height. Its angle of projection will be:
1. \(45^{\circ}\)
2. \(60^{\circ}\)
3. \(90^{\circ}\)
4. \(30^{\circ}\)

The maximum horizontal range of a projectile is \(400~\text{m}\). The maximum value of height(ever possible) attained by it will be: 
1. \(100~\text{m}\)
2. \(200~\text{m}\)
3. \(400~\text{m}\)
4. \(800~\text{m}\)

A particle is moving eastwards with a velocity of \(5\ \text{m/s}\). In \(10\) seconds, the velocity changes to \(5\ \text{m/s}\) northwards. The average acceleration in this time is:

1. Zero

2. \(\frac 1{\sqrt2} \ \text{m/s}^2\) toward north-west 

3. \(\frac 1{\sqrt2} \ \text{m/s}^2\) toward north-east

4. \(\frac 1{2} \ \text{m/s}^2\)​​​​​​​ toward north-west

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first

(1) 1, 2, 3, 4

(2) 2, 3, 4, 1

(3) 3, 4, 1, 2

(4) 4, 3, 2, 1

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 \(10\ \text{km/hr}\). He finds that raindrops are hitting his head vertically; the speed of raindrops with respect to the road will be:

1. \(10\ \text{km/hr}\)

2. \(20\ \text{km/hr}\) 

3. \(30\ \text{km/hr}\)

4. \(40\ \text{km/hr}\)

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