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 velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is- 

1. Zero

2. $\frac{1}{\sqrt{2}}m\text{/}{s}^{\text{2}}$ toward north-west

3. $\frac{1}{\sqrt{2}}m\text{/}{s}^{\text{2}}$ toward north-east

4. $\frac{1}{2}m\text{/}{s}^{\text{2}}$ 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 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 m/s at an angle of 120⁰ with the direction of flow of water. The speed of water in the stream is:

1. 1 m/s

2. 0.5 m/s

3. 0.25 m/s

4. 0.433 m/s

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