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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 $h_{2}?$
Motion in a Plane
Solution:
Range is same for angles of projection so $\theta=90 - \theta$
$R=\frac {u^{2}\,\,sin\,\,2\theta}{g}$
$h_{1}=\frac{u^{2}\,\,sin^{2}\,\,\theta}{2g}$ and $h_{2} =\frac{u^{2}\,\,cos^{2}\,\,\theta}{2g}$
Hence, $\sqrt{h_{1}h_{2}}= \frac{u^{2}\,\,sin\,\,\theta\,\,cos\,\, \theta}{2g}$
$=\frac{1}{4}[\frac{u^{2}\,\,sin^{2}\,\,2\theta}{g}]=\frac{R}{4}$