$A$ body projected from the ground reaches a point $X$ in its path after $3 \ s$ and from there it reaches the ground after a further $6 \ s$. The vertical distance of the point $X$ from the ground is (acceleration due to gravity $= 10 \ m/s^2$) (in $m$)

From the top of a tower, $80 \ m$ high from the ground, a stone is thrown in the horizontal direction with a velocity of $8 \ ms^{-1}$. The stone reaches the ground after a time $t$ and falls at a distance of $d$ from the foot of the tower. Assuming $g=10 \ ms^{-2}$, the time $t$ and distance $d$ are given respectively by

$A$ boy playing on the roof of a $10\, m$ high building throws a ball with a speed of $10\, m/s$ at an angle of $30^o$ with the horizontal. How far from the throwing point will the ball be at the height of $10\, m$ from the ground? $\left[ g = 10\, m/s^2, \sin 30^o = \frac{1}{2}, \cos 30^o = \frac{\sqrt{3}}{2} \right]$

$A$ body is projected horizontally from a tower with a velocity of $18 \, ms^{-1}$. It strikes the ground at an angle of $45^o$. The vertical component of the velocity when it strikes the ground is ........ $ms^{-1}$.

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The maximum height of the projectile is ........ $m$.

The vertical displacement ($y$ in metre) of a projectile in terms of its horizontal displacement ($x$ in metre) is given by $y = (\sqrt{3}x - 0.2x^2)$. The time of flight of the projectile is (Acceleration due to gravity $g = 10 \ ms^{-2}$)