If the time of flight of a projectile is $10 \ s$,and its range is $500 \ m$,then the maximum height attained by it will be ......... $m$.

$A$ body is projected at an angle $\theta$ with the horizontal. Another body is projected with the same speed at an angle $\theta$ with the vertical. The ratio of their maximum heights is:

$A$ batsman hits a ball with a velocity '$v$',making an angle of $60^{\circ}$ with the vertical. After some time, the direction of velocity makes an angle of $60^{\circ}$ with the horizontal. The speed of the ball at this instant is $[\cos(60^{\circ}) = \frac{1}{2}, \cos(30^{\circ}) = \frac{\sqrt{3}}{2}]$.

The horizontal and vertical displacements $x$ and $y$ of a projectile at a given time $t$ are given by $x = 6t \text{ m}$ and $y = 8t - 5t^2 \text{ m}$. The range of the projectile in metres is:

$A$ small ball is thrown at an angle $45^{\circ}$ to the horizontal with an initial velocity of $2 \sqrt{2} \ m/s$. The magnitude of the mean velocity averaged over the first $2 \ s$ is (take acceleration due to gravity $g = 10 \ m/s^2$). (in $m/s$)

$A$ cricketer can throw a ball to a maximum horizontal distance of $100 \; m$. How much high above (in $m$) the ground can the cricketer throw the same ball?