In a projectile motion, velocity at maximum height is

A particle is projected from a horizontal plane ($x-z$ plane) such that its velocity vector at time t is given by $\vec V = a\hat i + (b - ct)\hat j$ Its range on the horizontal plane is given by

The equation of motion of a projectile is $y = Ax -Bx^2$ where $A$ and $B$ are the constants of motion. The horizontal range of the projectile is

A projectile is thrown with an initial velocity of $(a \hat{ i }+b \hat{ j }) ms ^{-1}$. If the range of the projectile is twice the maximum height reached by it, then

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 $g=10 \;m s ^{-2}$ ).

The velocity of projectile at the intial point $A$ is $\left( {2\hat i + 3\hat j} \right)$ $m/s $ . It's velocity (in $m/s$) at point $B$ is