Range of a bullet fired at $45^o$ to the horizontal is $980 \, m$. If the bullet is fired at the same angle from a car travelling horizontally at $18 \, km/h$ towards the target,then the range will be increased by:

$A$ rod $P$ of length $1 \ m$ is hinged at one end $A$ and there is a ring attached to the other end by a light inextensible thread. Another long rod $Q$ is hinged at $B$ and it passes through the ring. The rod $P$ is rotated about an axis which is perpendicular to the plane in which both the rods are present and the variation between the angles $\theta$ and $\phi$ is plotted as shown. The distance between the hinges $A$ and $B$ is ........ $m$.

$A$ particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n u^2}{25 g}$,where the value of $n$ is (Given $g$ is the acceleration due to gravity).

Two bodies of mass $10 \, kg$ and $5 \, kg$ are moving in concentric orbits of radii $R$ and $r$ such that their periods are the same. What is the ratio of their centripetal accelerations?

$A$ particle is projected with velocity $u$ from point $M$ on a frictionless incline of length $20\sqrt{2} \, m$. If it crosses a $40 \, m$ wide well at an angle of $45^o$,what should be its velocity at point $M$?

$A$ particle moves around a circular path of radius $r$ with uniform speed $V$. After moving half the circle,the average acceleration of the particle is