If the time of flight of a bullet over a horizontal range R is T … - Vidyadip

MCQ

If the time of flight of a bullet over a horizontal range $R$ is $T\, seconds$, the inclination of the direction of projection to the horizontal is

A
${\sin ^{ - 1}}\,\left( {\frac{{g{T^2}}}{R}} \right)$
✓
${\tan ^{ - 1}}\,\left( {\frac{{g{T^2}}}{{2R}}} \right)$
C
${\cos ^{ - 1}}\,\left( {\frac{{2g{T^2}}}{{2R}}} \right)$
D
${\cot ^{ - 1}}\,\left( {\frac{R}{{g{T^2}}}} \right)$

✓

Answer

Correct option: B.

${\tan ^{ - 1}}\,\left( {\frac{{g{T^2}}}{{2R}}} \right)$

b
$\mathrm{R} \tan \theta=\frac{1}{2} \mathrm{g} \mathrm{T}^{2}$

$\tan \theta=\frac{\mathrm{g} \mathrm{T}^{2}}{2 \mathrm{R}}$

$\theta=\tan ^{-1} \frac{\mathrm{g} \mathrm{T}^{2}}{2 \mathrm{R}}$

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