A shell fired from the base of a mountain just clears it. If $\alpha$ is the angle of projection then the angular elevation of the summit $\beta$ is
$\frac{1}{2} \alpha$
$tan^{-1}(1/2)$
$tan^{-1}(1/2 \,\,tan \,\, \alpha )$
$tan^{-1}(2 \,\,tan\,\, \alpha )$
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 cricketer can throw a ball to a maximum horizontal distance of $100\, m .$ The speed with which he throws the ball is (to the nearest integer) (in $ms ^{-1}$)
A ball of mass $m$ is thrown vertically upward. Another ball of mass $2\,m$ is thrown an angle $\theta$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $\frac{1}{x}$. The value of $x$ is $.....$
A projectile crosses two walls of equal height $H$ symmetrically as shown The time of flight $T$ is given by ........ $\sec$
A stone is projected with a velocity $20 \sqrt{2}\,m / s$ at an angle of $45^{\circ}$ to the horizontal. The average velocity of stone during its motion from starting point to its maximum height is $..........\,m/s$ (take $g=10\,m / s ^2$ )