When a ball is thrown with a velocity of $50 \ m s^{-1}$ at an angle $30^{\circ}$ with the horizontal,it remains in the air for how many seconds? (Take $g = 10 \ m s^{-2}$)

It is possible to project a particle with a given velocity in two possible ways so as to make them pass through a point $P$ at a horizontal distance $r$ from the point of projection. If $t_1$ and $t_2$ are times taken to reach this point in two possible ways, then the product $t_1 t_2$ is proportional to

$A$ body is projected into a vertical $X-Y$ plane with the $X$-axis along the horizontal and the $Y$-axis along the vertical with an initial velocity $(10 \hat{i} + p \hat{j}) \ m/s$. If the maximum height reached by the body is $50 \%$ of its range,then the value of $p$ is:

Which one of the following statements is not true about the motion of a projectile?

$A$ ball projected at an angle of $45^{\circ}$ with the horizontal crosses two points at equal heights separated by a distance at times $2 \ s$ and $8 \ s$ respectively. The horizontal distance between the two points is (Acceleration due to gravity $= 10 \ m/s^2$) (in $m$)

If the equation of motion of a projectile is given by $y = 12x - \frac{3}{4}x^2$ and its horizontal component of velocity is $3 \ m/s$,then find its range. $(g = 10 \ m/s^2)$ (in $m$)