$A$ projectile is launched from the ground, such that it hits a target on the ground which is $90 \,m$ away. The minimum velocity of the projectile to hit the target is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-1}$)

$A$ cannon on a level plane is aimed at an angle $\theta$ above the horizontal and a shell is fired with a muzzle velocity $v_0$ towards a vertical cliff a distance $D$ away. Then the height from the bottom at which the shell strikes the side walls of the cliff is

An object is projected from the ground with a speed of $20 \, m/s$ at an angle of $30^{\circ}$ with the horizontal. Its centripetal acceleration one second after the projection is .......... $m/s^2$ [Take $g = 10 \, m/s^2$].

$A$ bullet is dropped from a certain height,and at the same instant,another bullet is fired horizontally from the same height. Which bullet will hit the ground first?

$A$ ball is thrown from the location $(x_0, y_0) = (0, 0)$ of a horizontal playground with an initial speed $v_0$ at an angle $\theta_0$ from the $+x$-direction. The ball is to be hit by a stone,which is thrown at the same time from the location $(x_1, y_1) = (L, 0)$. The stone is thrown at an angle $(180^{\circ} - \theta_1)$ from the $+x$-direction with a suitable initial speed $v$. For a fixed $v_0$,when $(\theta_0, \theta_1) = (45^{\circ}, 45^{\circ})$,the stone hits the ball after time $T_1$,and when $(\theta_0, \theta_1) = (60^{\circ}, 30^{\circ})$,it hits the ball after time $T_2$. In such a case,$(T_1 / T_2)^2$ is. . . . .

$A$ particle is projected with velocity $u$ at an angle $\alpha$ with the horizontal,and another particle is projected with the same velocity $u$ at an angle $\alpha$ with the vertical. What is the ratio of their times of flight?