The equation of motion of a projectile is given by \(x = 36 t\) metre and \(2y = 96 t – 9.8 t^2\) metre. The angle of projection is:

1. \(\sin^{− 1} \frac 45\)

2. \(\sin^{− 1} \frac 35\)

3. \(\sin^{− 1} \frac 43\)

4. \(\sin^{− 1} \frac 34\)${}^{}$

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 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. \(800~\text{m}\)

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