The trajectory of a projectile,projected from the ground,is given by $y = x - \frac{x^2}{20}$,where $x$ and $y$ are measured in meters. The maximum height attained by the projectile will be $...........\,m$.

Two bodies are projected with the same velocity. If one is projected at an angle of $30^\circ$ and the other at an angle of $60^\circ$ to the horizontal,the ratio of the maximum heights reached is

If $R$ and $H$ are the horizontal range and maximum height attained by a projectile,then its speed of projection is ..........

$A$ missile is fired for maximum range at your town from a place $100 \, km$ away from you. If the missile is first detected at its half-way point,how much warning time will you have? (Take $g = 10 \, m/s^2$)

Two projectiles are thrown with the same initial velocity making an angle of $45^{\circ}$ and $30^{\circ}$ with the horizontal,respectively. The ratio of their respective ranges will be:

The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta x^2$,where $\alpha$ and $\beta$ are constants and $x$ and $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by: