Neglecting the air resistance, the time of flight of a projectile is determined by:

1. \(U_{vertical}\)

2. \(U_{horizontal}\)

3. \(U = U^2_{vertical} + U^2_{horizontal}\)

4. \(U = (U^2_{vertical} + U^2_{horizontal} )^{1/2}\)

A ball is thrown from a point with a speed \(v_0\) at an angle of projection \(θ\). From the same point and at the same instant, a person starts running with a constant speed \(v_0/2\) to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

1. Yes, \(60^°\)

2. Yes, \(30^°\)

3. No

4. Yes, \(45^°\)

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

1. \(\sqrt{\dfrac{2H}{g}}\)

2. \( 2\sqrt{\dfrac{2H}{g}}\)

3.  \(\dfrac{2\sqrt{2H}\sin\theta}{g}\)

4. \(\dfrac{\sqrt{2H}\sin\theta}{g}\)

The horizontal range of a projectile is \(4 \sqrt{3}\) times its maximum height. Its angle of projection will be:
1. \(45^{\circ}\)
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 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. \(5\sqrt{2}\)