The equation of motion of a projectile is $y = 12x - \frac{5}{9}x^2$. The horizontal component of velocity is $3 \ ms^{-1}$. Given that $g = 10 \ ms^{-2}$,the range of the projectile is .......... $m$.

Neglecting air resistance,the time of flight of a projectile is determined by:

$A$ projectile is fired at $30^{\circ}$ to the horizontal. The vertical component of its velocity is $80 \; ms^{-1}$. Its time of flight is $T$. What will be the velocity of the projectile at $t = \frac{T}{2}$?

$A$ particle having kinetic energy $K$ is projected at $60^{\circ}$ with the horizontal. The kinetic energy at the highest point is

$A$ 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 $2 \sqrt{gh}$,so that it just flies over two walls of equal height $h$ and $2h$ distance apart from each other. Find the time for which the particle flies between the walls.