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Q.
A person can throw a stone to a maximum distance of $500\, m$. The greatest height to which he can throw the stone is:
Motion in a Plane
Solution:
Maximum height is given by $H =\frac{ u ^2 \sin ^2 \theta}{2 g }$
Range is given as $R =\frac{ u ^2 \sin 2 \theta}{ g }=100 m$ (given)
Maximum height is attained at 45 degree launch, so $\theta=45$
$u ^2=1000$ and Maximum height is $25 m$ by formula of $H$.