A projectile cover double range as compare to its maximum height attained. The angle of projection is
$\tan^{-1} \,2$
$\tan^{-1} \,4$
$\tan^{-1} \,3$
$\tan^{-1} \,5$
A boy playing on the roof of a $10\, m$ high building throws a ball with a speed of $10\, m/s$ at an angle $30^o$ with the horizontal. ........ $m$ far from the throwing point will the ball be at the height of $10\, m$ from the ground . $(g \,= \,10 m/s^2, \,sin \,30^o \,= \,\frac{1}{2}$, $\cos \,{30^o}\, = \,\frac{{\sqrt 3 }}{2}$)
A cricketer can throw a ball to a maximum horizontal distance of $100\, m$. The speed with which he throws the ball is ......... $ms^{-1}$ (to the nearest integer)
A cannon on a level plane is aimed at an angle $\theta $ above the horizontal and a shell is fired with a muzzle velocity ${v_0}$ towards a vertical cliff a distance $D$ away. Then the height from the bottom at which the shell strikes the side walls of the cliff is
The horizontal range of a projectile is $4\sqrt 3 $ times its maximum height. Its angle of projection will be ......... $^o$
A projectile is launched from the origin in the $xy$ plane ( $x$ is the horizontal and $y$ is the vertically up direction) making an angle $\alpha$ from the $x$-axis. If its distance. $r =\sqrt{ x ^2+ y ^2}$ from the origin is plotted against $x$, the resulting curves show different behaviours for launch angles $\alpha_1$ and $\alpha_2$ as shown in the figure below. For $\alpha_1, r ( x )$ keeps increasing with $x$ while for $\alpha_2$, $r(x)$ increases and reaches a maximum, then decreases and goes through a minimum before increasing again. The switch between these two cases takes place at an angle $\alpha_c\left(\alpha_1 < \alpha_c < \alpha_2\right)$. The value of $\alpha_c$ is [ignore where $v_0$ is the initial speed of the projectile and $g$ is the acceleration due to gravity]