For a given velocity, a projectile has the same range of \(R\) for two angles of projection. If \(t_1\) and \(t_2\) are the times of flight in the two cases then:
1. \(t_1t_2 \propto R^2\)

2. \(t_1t_2 \propto R\)

3. \(t_1t_2 \propto \dfrac{1}{R}\)

4. \(t_1t_2 \propto \dfrac{1}{R^2}\)

A body of mass \(m\) is thrown upwards at an angle \(θ\) with the horizontal at velocity \(v\). While rising, the velocity of the mass after \(t\) seconds will be:

1. \(\sqrt{(v\cos\theta)^2+(v\sin\theta)^2}\)

2. \(\sqrt{(v\cos\theta-v\sin\theta)^2-gt}\)

3. \(\sqrt{v^2+g^2t^2-(2v\sin\theta)gt}\)

4. \(\sqrt{v^2+g^2t^2-(2v\cos\theta)gt}\)

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. \(50~\text{m}\)

A ball is projected with velocity \(v_0\) at an angle of elevation \(30^°\). Mark the correct statement.

1. Kinetic energy will be zero at the highest point of the trajectory.

2. Vertical component of momentum will be conserved.

3. Horizontal component of momentum will be conserved.

4. Gravitational potential energy will be minimum at the highest point of the trajectory.

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