A projectile is projected at $30^{\circ}$ from horizontal with initial velocity $40\,ms ^{-1}$. The velocity of the projectile at $t =2\,s$ from the start will be $........$ (Given $g =10\,m / s ^2$ )

A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is

A projectile thrown with velocity $v$ making angle $\theta$ with vertical gains maximum height $H$ in the time for which the projectile remains in air, the time period is

An object is projected at an angle of $45^°$ with the horizontal. The horizontal range and the maximum height reached will be in the ratio.

A ball is thrown from the ground to clear a wall $3\,m$ high at a distance of $6\,m$ and falls $18\,m$ away from the wall, the angle of projection of ball is

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first