Question
The maximum horizontal range of a projected object is R. What is maximum height it reaches?

Answer

If $\theta=45^{\circ}$ then
$\begin{aligned}
H & =\frac{1}{4}\left(\frac{u^2}{g}\right) \\
R_{\max } & =\frac{u^2}{g} \\
H & =\frac{R_{\max }}{4}
\end{aligned}$

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