An object is thrown along a direction inclined at an angle of $45^\circ$ with the horizontal direction. The horizontal range of the particle is equal to

If the kinetic energy of a second ball at its maximum height is $K$,what will be the kinetic energy of the first ball at its maximum height? (Assuming the first ball is thrown vertically upwards).

The ratio of minimum kinetic energies of two projectiles of the same mass is $4:1$. The ratio of the maximum heights attained by them is also $4:1$. The ratio of their ranges would be: (in $:1$)

The trajectory of a projectile projected from the origin is given by the equation $y = x - \frac{2x^2}{5}$. The initial velocity of the projectile is:

Two stones are thrown with the same speed $u$ at different angles from the ground into the air. If both stones have the same range and the heights attained by them are $h_1$ and $h_2$,then $h_1 + h_2$ is equal to .......

The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5t^2) \text{ m}$ and $x = 6t \text{ m}$,where $t$ is in seconds. The acceleration due to gravity on this planet is ......... $m/s^2$.