Question
Maximum height of projectile is H and tim of flight is $T$. Prove that $8 H =g T^2$.
✓
Answer
$\text { R.H.S. }=g T^2=g\left(\frac{2 u \sin \theta}{g}\right)^2$
(Keeping the value of flight time T)
$\begin{array}{l}
=\frac{2 \times 4 u^2 \sin ^2 \theta}{g^2} \\
=\frac{2 \times 4 u^2 \sin ^2 \theta}{2 g}
\end{array}$
(Multiplying numerator and denominator by 2 )
$=\frac{8 u^2 \sin ^2 \theta}{2 g}$....(1)
But maximum height, $H =\frac{u^2 \sin ^2 \theta}{2 g}$
From equation (1) $\quad g T^2=8 H \quad$ Hence Proved.
(Keeping the value of flight time T)
$\begin{array}{l}
=\frac{2 \times 4 u^2 \sin ^2 \theta}{g^2} \\
=\frac{2 \times 4 u^2 \sin ^2 \theta}{2 g}
\end{array}$
(Multiplying numerator and denominator by 2 )
$=\frac{8 u^2 \sin ^2 \theta}{2 g}$....(1)
But maximum height, $H =\frac{u^2 \sin ^2 \theta}{2 g}$
From equation (1) $\quad g T^2=8 H \quad$ Hence Proved.
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