Three balls of same masses are projected with equal speeds at angles $15^{\circ}, 45^{\circ}$,and $75^{\circ}$. If their ranges are $R_1, R_2$,and $R_3$ respectively,then:

$A$ shell fired from the base of a mountain just clears it. If $\alpha$ is the angle of projection,then the angular elevation of the summit $\beta$ is

The equation of a projectile is given by $y = Px - Qx^2$,where $P$ and $Q$ are constants. The ratio of the maximum height to the range of the projectile is

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 $:1$)

$A$ football player throws a ball with a velocity of $50 \ m/s$ at an angle of $30^{\circ}$ from the horizontal. The ball remains in the air for ...... $s$ $(g = 10 \ m/s^2)$.

Assume that the acceleration due to gravity on the surface of the moon is $0.2$ times the acceleration due to gravity on the surface of the earth. If $R_e$ is the maximum range of a projectile on the earth's surface,what is the maximum range on the surface of the moon for the same velocity of projection (in $,R_e$)?