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 $g = 10\ ms^{- 2}$ , .......... $m$ is the range of the projectile .

A heavy particle is projected from a point on the horizontal at an angle $60^o$ with the horizontal with a speed of $10\ m/s$ . Then the radius of the curvature of its path at the instant of crossing the same horizontal will be    ......... $m$

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

A projectile is thrown upward with a velocity $v_0$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is

A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is

Two particles $A$ and $B$ are moving in horizontal plane as shown in figure at $t = 0$ , then time after which $A$ will catch $B$ will be.......$s$