$A$ body projected along a frictionless inclined plane of angle of inclination $30^{\circ}$ covers a distance of $40\, m$ along the plane. If the body is projected with the same speed at an angle of $30^{\circ}$ with the ground,it will have a range of: (Take $g = 10\, m/s^2$)

$A$ particle moves along a circle with a constant angular speed $\omega$. Its displacement,with respect to the initial position of the particle at time $t = 0$,is plotted against time. The graph would look like:

$A$ racing car is moving with velocity $v = 40\ m/s$ on a straight track as shown. We are recording it with a camera placed at a distance of $30\ m$ from the road. Find the angular velocity (in $rad/s$) with which we should rotate the camera to record the race at the instant shown in the diagram.

The position coordinates of a projectile projected from the ground on a certain planet (with no atmosphere) are given by $y = (4t - 2t^2) \text{ m}$ and $x = (3t) \text{ m}$,where $t$ is in seconds and the point of projection is taken as the origin. The angle of projection of the projectile with the vertical is ......... (in $^{\circ}$)

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The height of each wall is ........ $m$.

$A$ projectile of mass $m$ is fired with velocity $v$ from the point $P$ at an angle $45^{\circ}$ with the horizontal. The magnitude of change in momentum,when it passes through the point $Q$ on the same horizontal line on which $P$ lies,is :