An arrow is shot into the air. Its range is $200\,m$ and its time of flight is $5\,s$. If $g=10\,m/s^2$,then the horizontal component of velocity and the maximum height will be respectively:

$A$ cart is moving horizontally along a straight line with a constant speed of $30\,m/s$. $A$ projectile is to be fired from the moving cart in such a way that it will return to the cart (at the same point on the cart) after the cart has moved $80\,m$. At what velocity (relative to the cart) must the projectile be fired? (Take $g = 10\,m/s^2$)

$A$ cricketer can throw a ball to a maximum horizontal distance of $100 \, m$. With the same effort,he throws the ball vertically upwards. The maximum height attained by the ball is ......... $m$.

$A$ particle covers $50\, m$ distance when projected with an initial speed. On the same surface,it will cover a distance of ......... $m$ when projected with double the initial speed.

Two paper screens $A$ and $B$ are separated by a distance of $100 \,m$. $A$ bullet penetrates $A$ and $B$ at points $P$ and $Q$ respectively,where $Q$ is $10 \,cm$ below $P$. If the bullet is travelling horizontally at the time of hitting $A$,the velocity of the bullet at $A$ is nearly .......... $m/s$.

$A$ 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: