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?
Their maximum height will be same
Their range will be same
Their landing velocity will be same
Their time of flight will be same
Two projectiles are projected at $30^{\circ}$ and $60^{\circ}$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:
The time of flight of an object projected with speed $20 \,ms ^{-1}$ at an angle $30^{\circ}$ with the horizontal, is .... $s$
A particle is projected from ground at an angle $\theta$ with horizontal with speed $u$. The ratio of radius of curvature of its trajectory at point of projection to radius of curvature at maximum height is ........
A fighter plane flying horizontally at an altitude of $1.5\; km$ with speed $720\; km / h$ passes directly overhead an anti-atrcraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed $600\; m s ^{-1}$ to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit ? (Take $g=10 \;m s ^{-2}$ ).
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]