$A$ body is thrown horizontally from the top of a tower of height $5 \, m$. It touches the ground at a distance of $10 \, m$ from the foot of the tower. The initial velocity of the body is ......... $m/s$ $(g = 10 \, m/s^2)$.

$A$ cricketer can throw a ball to a maximum horizontal distance of $100 \; m$. How much high above (in $m$) the ground can the cricketer throw the same ball?

$A$ ball is dropped from a high tower,and another ball is thrown horizontally from the same position. Which ball will reach the ground first?

$A$ stone is projected in air. Its time of flight is $3\,s$ and range is $150\,m$. The maximum height reached by the stone is $......\,m$ $\left(g=10\,m/s^2\right)$.

Two towers $A$ and $B$,each of height $20 \ m$,are situated a distance $200 \ m$ apart. $A$ body thrown horizontally from the top of the tower $A$ with a velocity $20 \ ms^{-1}$ towards the tower $B$ hits the ground at point $P$,and another body thrown horizontally from the top of tower $B$ with a velocity $30 \ ms^{-1}$ towards the tower $A$ hits the ground at point $Q$. If a car starting from rest from $P$ reaches $Q$ in $10 \ s$,then the acceleration of the car is (acceleration due to gravity $g = 10 \ ms^{-2}$): (in $ms^{-2}$)

The initial velocity of a projectile is given by $v = a\hat{i} + b\hat{j}$. If the range $R$ is twice the maximum height $H$,then which of the following is true?