A projectile is thrown at an angle $\theta$ such that it is just able to cross a vertical wall at its highest point as shown in the figure.The angle $\theta$ at which the projectile is thrown is given by
$\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
$\tan ^{-1}(\sqrt{3})$
$\tan ^{-1}\left(\frac{2}{\sqrt{3}}\right)$
$\tan ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5{t^2})$ meter and $x = 6t\, meter$, where $t$ is in second. The velocity with which the projectile is projected is ......... $m/sec$.
A projectile is fired at $30^{\circ}$ to the horizontal, The vertical component of its velocity is $80 \;ms ^{-1}$, Its time flight is $T$. What will be the velocity of projectile at $t =\frac{ T }{2}$?
A projectile crosses two walls of equal height $H$ symmetrically as shown The height of each wall is ........ $m$
An insect trapped in a circular groove of radius $12 \;cm$ moves along the groove steadily and completes $7$ revolutions in $100\; s$.
$(a)$ What is the angular speed, and the linear speed of the motion?
$(b)$ Is the acceleration vector a constant vector ? What is its magnitude ?
A player throws a ball that reaches to the another player in $4\,s$. If the height of each player is $1.5\,m$, the maximum height attained by the ball from the ground level is .......... $m$