A projectile fired at $30^{\circ}$ to the ground is observed to be at same height at time $3 s$ and $5 s$ after projection, during its flight. The speed of projection of the projectile is $………\,ms ^{-1}$(Given $g=10\,m s ^{-2}$ )

If time of flight of a projectile is $10$ seconds. Range is $500$ meters. The maximum height attained by it will be  ……… $m$

A particle is projected in air at some angle to the horizontal, moves along parabola as shown in figure where $x$ and $y$ indicate horizontal and vertical directions respectively. Shown in the diagram, direction of velocity and acceleration at points $A, \,B$ and $C$.

A particle is projected at angle $\theta$ with horizontal from ground. The slop $(m)$ of the trajectory of the particle varies with time $(t)$ as ………..

The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t – 5{t^2})$ meter and $x = 6t\, meter$, where $t$ is in second. The velocity with which the projectile is projected is ……… $m/sec$.