For a given angle of the projectile if the initial velocity is doubled the range of the projectile becomes

The range of a projectile for a given initial velocity is maximum when the angle of projection is ${45^o}$. The range will be minimum, if the angle of projection is ......... $^o$

A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is

Two projectiles $A$ and $B$ are thrown with the same speed but angles are $40^{\circ}$ and $50^{\circ}$ with the horizontal. Then

A particle is projected from ground at an angle $\theta$ with horizontal with speed $u$. The ratio of radius of curvature of its trajectory at point of projection to radius of curvature at maximum height is ........

A projectile is thrown at an angle $\theta$ such that it is just able to cross a vertical wall at its highest point as shown in the figure.The angle $\theta$ at which the projectile is thrown is given by