A projectile is fired from level ground at an angle $\theta $ above the horizontal. The elevation angle $\phi $ of the highest point as seen from the launch point is related to $\theta $ by the relation
$\tan \,\phi = \frac{1}{4}\,\tan \,\theta $
$\tan \,\phi = \tan \,\theta $
$\tan \,\phi = \frac{1}{2}\,\tan \,\theta $
$\tan \,\phi = 2\,\tan \,\theta $
A ball is projected from ground at an angle $45^{\circ}$ with horizontal from distance $d_1$ from the foot of a pole and just after touching the top of pole it the falls on ground at distance $d_2$ from pole on other side, the height of pole is ...........
A wheel of radius $R$ is trapped in a mud pit and spinning. As the wheel is spinning, it splashes mud blobs with initial speed $u$ from various points on its circumference. The maximum height from the centre of the wheel, to which a mud blob can reach is
Four bodies $P, Q, R$ and $S$ are projected with equal velocities having angles of projection $15^{\circ}, 30^{\circ}, 45^{\circ}$ and $60^{\circ}$ with the horizontals respectively. The body having shortest range is
In the given figure for a projectile
An object is projected from ground with speed $u$ at angle $\theta$ with horizontal. the radius of curvature of its trajectory at maximum height from ground is ..........