Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?

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 .

The position of a projectile launched from the origin at $t = 0$ is given by $\vec r = \left( {40\hat i + 50\hat j} \right)\,m$ at $t = 2\,s$. If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is (take $g = 10\, ms^{-2}$)

A particle moves in a plane with constant acceleration in a direction different from the initial velocity. The path of the particle will be

A particle is projected with an angle of projection $\theta$ to the horizontal line passing through the points $( P , Q )$ and $( Q , P )$ referred to horizontal and vertical axes (can be treated as $x$-axis and $y$-axis respectively).

The angle of projection can be given by

A projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80\,m / s$. Its time of flight is $T$. Its velocity at $t=\frac{T}{4}$ has a magnitude of nearly $........\frac{m}{s}$