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
$\frac{1}{2} \alpha$
$tan^{-1}(1/2)$
$tan^{-1}(1/2 \,\,tan \,\, \alpha )$
$tan^{-1}(2 \,\,tan\,\, \alpha )$
Two projectiles are fired from the same point with the same speed at angles of projection $60^o$ and $30^o$ respectively. Which one of the following is true?
A particle is projected from ground with speed $80 \,m / s$ at angle $30^{\circ}$ with horizontal from ground. The magnitude of average velocity of particle in time interval $t=2 \,s$ to $t=6 \,s$ is ....... $m / s$ [Take $g=10 \,m / s ^2$ ]
At $t = 0$ a projectile is fired from a point $O$(taken as origin) on the ground with a speed of $50\,\, m/s$ at an angle of $53^o$ with the horizontal. It just passes two points $A \& B$ each at height $75 \,\,m$ above horizontal as shown The distance (in metres) of the particle from origin at $t = 2$ sec.
Four bodies $P, Q, R$ and $S$ are projected with equal velocities having angles of projection $15^o , 30^o , 45^o $ and $60^o $ with the horizontal respectively. The body having shortest range is
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