Which of the following sets of factors will affect the horizontal distance covered by an athlete in a long–jump event?
1. speed before he jumps and his weight
2. the direction in which he leaps and the initial speed
3. the force with which he pushes the ground and his speed
4. none of the above

A cricketer can throw a ball to a maximum horizontal distance of \(100~\text{m}\). With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is: 
1. \(100~\text{m}\)
2. \(80~\text{m}\)
3. \(60~\text{m}\)
4. \(50~\text{m}\)

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. \(30^{\circ}\)

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 \(3\hat i + 4\hat j\) 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 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 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