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:

In a sports competition,a javelin is thrown at an angle $45^{\circ}$,which recorded a range of $90 \,m$. The maximum height reached by the javelin is (Neglect air resistance and acceleration due to gravity $g = 10 \,ms^{-2}$)

$A$ particle is projected with an angle of projection $\theta$ to the horizontal. The trajectory passes through the points $(P, Q)$ and $(Q, P)$ referred to horizontal and vertical axes ($x$-axis and $y$-axis respectively). The angle of projection $\theta$ is given by:

$A$ body of mass $1 \, kg$ is projected from the ground at an angle of $30^{\circ}$ with the horizontal on level ground at a speed of $50 \, m/s$. The magnitude of the change in momentum of the body during its entire flight is ....... $kg \cdot m/s$ $(g = 10 \, m/s^2)$.

$A$ projectile is fired with a speed $u$ at an angle $\theta$ with the horizontal. Its speed when its direction of motion makes an angle $\alpha$ with the horizontal is

For a projectile,the ratio of the maximum height reached to the square of the time of flight is: