At the top of the trajectory of a projectile, the directions of its velocity and acceleration are:

The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\)m/s. Its velocity (in m/s) at point \(B\) is:
              

A stone projected with a velocity \(u\) at an angle \(\theta\) with the horizontal reaches maximum height \(H_1\). When it is projected with velocity \(u\) at an angle \(\frac{\pi}{2}-\theta\) with the horizontal, it reaches maximum height \(H_2\). The relation between the horizontal range of the projectile \(R\) and \(H_1\) & \(H_2\) is: 

A missile is fired for a maximum range with an initial velocity of \(20\) m/s. If \(g=10\) m/s², then the range of the missile will be:
1. \(50\) m
2. \(60\) m
3. \(20\) m
4. \(40\) m

A ball is projected at a certain angle with initial velocity \(u\). It covers horizontal range \(R\). With what initial velocity it should be projected keeping the angle of projection the same so that its horizontal range becomes \(2.25R\)?

For a projectile projected at angles \((45^{\circ}-\theta)\) and \((45^{\circ}+\theta)\), the horizontal ranges described by the projectile are in the ratio of:
1. \(1:1\)
2. \(2:3\)
3. \(1:2\)
4. \(2:1\)

An aeroplane is moving with a velocity \(u\). It drops a packet from a height \(h\). The time \(t\) taken by the packet to reach the ground will be:
1. \( \sqrt{\left(\frac{2 g}{h}\right)} \)
2. \( \sqrt{\left(\frac{2 u}{g}\right)} \)
3. \( \sqrt{\left(\frac{h}{2 g}\right)} \)
4. \( \sqrt{\left(\frac{2 h}{g}\right)}\)

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by
\(y =4 t - 2 t^{2}~ \text{m}\)  and \(x =3t\) metre, where \(t\) is in seconds and point of projection is taken as the origin. The angle of projection of projectile with vertical is:
1. \(30^{\circ}\)
2. \(37^{\circ}\)
3. \(45^{\circ}\)
4. \(60^{\circ}\)

If two projectiles, with the same masses and with the same velocities, are thrown at an angle \(60^\circ\) & \(30^\circ\) with the horizontal, then which of the following quantities will remain the same?

The equation of trajectory of a projectile is given by \(y = x-10x^{2}\). Its speed of projection is: (\(g =1 0\) m/${\mathrm{s}}^2$)
1. \(1\) m/s
2. \(2\) m/s
3. \(3\) m/s
4. \(4\) m/s