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Q.
A cricketer can throw a ball to a maximum horizontal distance of $d$. How high above the ground can the cricketer throw the same ball?
Motion in a Straight Line
Solution:
Let $u$ is the velocity of projection, then
$R _{\max }=\frac{ u ^{2}}{ g }= d$ or $u =\sqrt{ gd }$
Let $h$ is the height upto which ball rise, then
$0=u^{2}-2 g h$
or $h=\frac{u^{2}}{2 g}=\frac{g d}{2 g}=\frac{d}{2}$