The initial speed of a bullet fired from a rifle is $630 \; m/s$. The rifle is fired at the center of a target $700 \; m$ away at the same level as the target. How far above the center of the target (in $m$) must the rifle be aimed in order to hit the target? (Take $g = 10 \; m/s^2$)

$A$ large number of bullets are fired in all directions with the same speed $u$. The maximum area of the ground on which these bullets spread is ($g$ - acceleration due to gravity).

Two guns $A$ and $B$ can fire bullets at speeds $1 \ km/s$ and $2 \ km/s$ respectively. From a point on a horizontal ground,they are fired in all possible directions. The ratio of the maximum areas covered by the bullets fired by the two guns on the ground is

The top of a smooth inclined plane of length $20 \sqrt{2} \,m$ is connected to the edge of a well of diameter $40 \,m$ making an angle $45^{\circ}$ with the vertical as shown in the figure. $A$ body is projected along the inclined plane with a velocity '$u$'. If the body crosses the well without falling into it, then the minimum value of '$u$' is $(g=10 \,ms^{-2})$.

$A$ boy throws a ball with a velocity $u$ at an angle $\theta$ with the horizontal. At the same instant,he starts running with a uniform velocity to catch the ball before it hits the ground. To achieve this,he should run with a velocity of

For a given velocity,a projectile has the same range $R$ for two angles of projection. If $t_1$ and $t_2$ are the times of flight in the two cases,then: