At what angle should a particle be projected to cover the maximum range (in $^{\circ}$)?

An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range $R$ is maximum. Another object is projected in the air with a horizontal range half of the range of the first object. The initial velocity remains the same in both cases. The value of the angle of projection,at which the second object is projected,will be $.......$ degrees.

$A$ bomb of mass $m$ is projected from the ground with speed $v$ at an angle $\theta$ with the horizontal. At the maximum height from the ground,it explodes into two fragments of equal mass. If one fragment comes to rest immediately after the explosion,then the horizontal range of the centre of mass is ..............

The maximum horizontal range of a projectile is $160 \ m$. When the projectile is thrown with the same speed at an elevation of $30^{\circ}$ from the horizontal,it will reach a maximum height of ......... $m$.

$A$ bomb is dropped on an enemy post on the ground by an aeroplane flying horizontally with a velocity of $60 \ km/h$ at a height of $490 \ m$. At the time of dropping the bomb, the horizontal distance of the aeroplane from the enemy post so that the bomb hits the target is

If $R$ and $H$ are the horizontal range and maximum height attained by a projectile,then its speed of projection is ..........