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3-2.Motion in Plane
medium
If $R$ and $H$ represent the horizontal range and the maximum height achieved by a projectile then which of the relation exists?
A
$\frac{H}{R} = 4\,\cot \,\theta $
B
$\frac{R}{H} = 4\,\cot \,\theta $
C
$\frac{H}{R} = 4\,\tan \,\theta $
D
$\frac{R}{H} = 4\,\tan \,\theta $
(AIIMS-2009)
Solution
$\begin{array}{l}
R = \frac{{{u^2}\sin 2\theta }}{g} = \frac{{2{u^2}\sin \theta .\cos \theta }}{g}\\
H = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}\\
\therefore \,\frac{H}{R} = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}} \times \frac{g}{{2{u^2}\sin \theta .\cos \theta }}\\
\,\,\,\,\,\,\,\,\,\,\, = \frac{{\sin \theta }}{{4\cos \theta }}\\
\Rightarrow \frac{R}{H} = \frac{{4\cos \theta }}{{\sin \theta }}\,or\,,\,\frac{R}{H} = 4\cos \theta
\end{array}$
Standard 11
Physics
