A boy, standing at a certain height, kicks a football horizontally with a velocity of $19.6 \mathrm{~ms}^{-1}$. What will be the ratio of horizontal and vertical components of velocities after $2 s$ ?

A particle moves along a parabolic path $y=9 x^2$ in such a way that the x component of velocity remains constant. If, the acceleration of the particle is $2 j m s^{-2}$, find the x component of velocity.

An object is dropped from a certain point A at a height ' h ' from the ground. During it's journey straight downwards, the object passes points $B$ and $C$ such that the ratio of time taken $t_1$ to cover $A B$ and $t_2$ to cover $B C$ is $1:(\sqrt{2}-1)$. What is the ratio of distances $A B: B C$ ?

A car, starting from rest, accelerates at a rate of $\beta$ through a distance S , then continues at constant speed for time t and then decelerates at a rate of $\frac{\beta}{2}$ to come to rest. If the total distance travelled is $10 S$, then ratio $\frac{S}{t^2}$ is