The horizontal range of a projectile is $4\sqrt{3}$ times its maximum height. Its angle of projection will be:

1. 45°

2. 60°

3. 90°

4. 30°

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

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 3i + 4j with respect to ground. The water in the river is moving with a velocity – 3i – 4j with respect to ground. The relative velocity of the boat with respect to water is 

1. 8j

2. – 6i – 8j

3. 6i +8j

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 10m/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

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 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

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

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

A particle moves towards east with velocity 5 m/s. After 10 seconds its direction changes towards north with same velocity. The average acceleration of the particle is 

(1) Zero

(2) $\frac{1}{\sqrt{2}}m/s^{2}N-W$

(3) $\frac{1}{\sqrt{2}}m/s^{2}N-E$

(4) $\frac{1}{\sqrt{2}}m/s^{2}S-W$