A projectile is projected with kinetic energy $K$. If it has the maximum possible horizontal range, then its kinetic energy at the highest point will be ......... $K$

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

A cricketer can throw a ball to maximum horizontal distance of $100\,m$ . With the same speed how much high above the ground can the cricketer throw the same ball   ......... $m$

A very broad elevator is going up vertically with a constant acceleration of $2\,m / s ^2$. At the instant when its velocity is $4\,m / s$ a ball is projected from the floor of the lift with a speed of $4\,m / s$ relative to the floor at an elevation of $30^{\circ}$. The time taken by the ball to return the floor is $..............\,s$ $\left(g=10\,m / s ^2\right)$

A ball projected from ground at an angle of $45^o$ just clears a wall in front. If point of projection is $4\,m$ from the foot of wall and ball strikes the ground at a distance of $6\,m$ on the other side of the wall, the height of the walI is  ........ $ m$

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