The horizontal range is four times the maximum height attained by a projectile. The angle of projection is  .......... $^o$

A ball is projected from the ground with a speed $15 \,ms ^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then $tan\,\theta$ will be equal to 

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

In a projectile motion, velocity at maximum height is

A projectile is fired at a speed of $100\, m/sec$ at an angle of $37^o$ above the horizontal. At the highest point, the projectile breaks into two parts of mass ratio $1:3$, the smaller coming to rest. Then the distance of heavier part from the launching point is ........... $m$.

A ball of mass $1 \;kg$ is thrown vertically upwards and returns to the ground after $3\; seconds$. Another ball, thrown at $60^{\circ}$ with vertical also stays in air for the same time before it touches the ground. The ratio of the two heights are