Question

If $R$ and $H$ are the horizontal range and maximum height attained by a projectile, than its speed of projection is:

• A. $\sqrt{2gR+\frac{4R^2}{gH}}$
• B. $\sqrt{2gH+\frac{R^{2}g}{8H}}$
• C. $\sqrt{2gH+\frac{8H}{Rg}}$
• D. $\sqrt{2gH+\frac{R^2}{H}}$

Answer 1

The correct option is B $\sqrt{2gH+\frac{R^{2}g}{8H}}$

$H=\frac{u^{2}si{n}^2\theta }{2g}$

$R=\frac{u^{2}sin2\theta }{g}$

$co{s}^2\theta =\frac{R^{2}g}{8u^{2}H}$

$si{n}^2\theta =\frac{2Hg}{u^2}$

$si{n}^2\theta +si{n}^2\theta =1$

$u=\sqrt{\frac{R^{2}g}{8H}+2Hg}$