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  4. The range R of projectile is same when its maximum heights are h1 and h2 . What is the relation between R , h1 and h2 ?

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Q. The range $R$ of projectile is same when its maximum heights are $h_{1}$ and $h_{2} .$ What is the relation between $R , h_{1}$ and $h_{2}$ ?

Solution:

Range is same for angles of projection $\theta$ and $90-\theta$.
$\therefore R=\frac{u^{2} \sin 2 \theta}{g} ; h_{1}=\frac{u^{2} \sin ^{2} \theta}{2 g}$
and $h_{2}=\frac{u^{2} \cos ^{2} \theta}{2 g}$
Hence, $\sqrt{h_{1} h_{2}}=\frac{u^{2} \sin \theta \cos \theta}{2 g}$
$=\frac{1}{4}\left[\frac{u^{2} \sin 2 \theta}{g}\right]=\frac{R}{4}$