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Q.
A man can throw a stone to a maximum distance of $80\, m$. The maximum height to which it will rise, is
Motion in a Plane
Solution:
Given , maximum horizontal range, $R_{\max }=80 \,m$
As, range of a projectile, $R=\frac{u^{2} \sin 2 \theta}{g}$
and it is maximum $\theta=45^{\circ}$
$\therefore \quad \frac{u^{2}}{g}=80 \, m$
Maximum height, $h=\frac{u^{2} \sin ^{2} \theta}{2 g}$
$=\frac{80}{2}\left(\sin ^{2} 45^{\circ}\right)=40 \times \frac{1}{2}=20 \, m$