$A$ large number of bullets are fired in all directions with the same speed $u$. The maximum area on the ground on which the bullets will spread is

$A$ particle is thrown with a speed of $12 \, m/s$ at an angle $60^o$ with the horizontal. The time interval between the moments when its speed is $10 \, m/s$ is $(g = 10 \, m/s^2)$.........$s$

$A$ particle is projected from level ground. Its kinetic energy $K$ changes due to gravity such that $\frac{K_{\max}}{K_{\min}} = 9$. The ratio of the range $R$ to the maximum height $H$ attained during its flight is:

$A$ ball rolls off the top of a stairway with horizontal velocity $u$. The steps are $0.1 \ m$ high and $0.1 \ m$ wide. The minimum velocity $u$ with which the ball just hits the $5^{\text{th}}$ step of the stairway will be $\sqrt{x} \ ms^{-1}$ where $x=$ . . . . . . [use $g=10 \ ms^{-2}$].

An aeroplane is flying at a constant horizontal velocity of $600\, km/hr$ at an elevation of $6\, km$ towards a point directly above the target on the earth's surface. At an appropriate time,the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling

$A$ ball is projected from the ground with a speed $15 \, m/s$ at an angle $\theta$ with the horizontal such that its range and maximum height are equal. Then,$\tan \theta$ will be equal to: