A stone is thrown at an angle θ with the horizontal reaches a maximum height of H. Then the time of flight of stone will be:

(1) $\sqrt{\frac{2H}{g}}$

(2) $2\sqrt{\frac{2H}{g}}$

(3) $\frac{2\sqrt{2H\sin \theta }}{g}$

(4) $\frac{\sqrt{2H\sin \theta }}{g}$

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°

The maximum horizontal range of a projectile is 400 m. The maximum value of height(ever possible) attained by it will be 

(1) 100 m

(2) 200 m

(3) 400 m

(4) 800 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 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