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  • A projectile can have the same range   for angles of projection. It  <img a

A projectile can have the same range \mathrm { R }  for angles of projection. It  \mathrm{t_1 \: and \: \: t_2}  be the times of flight in the two cases, then what is the product of two times of flight?

Option: 1

\mathrm{ t_1 t_2 \propto R^2}


Option: 2

\mathrm{ t_1 t_2 \propto \frac{1}{R}}


Option: 3

\mathrm{ t_1 t_2 \propto R}


Option: 4

\mathrm{t_1 t_2 \propto \frac{1}{R^2}}


Answers (1)

best_answer

 For same range \mathrm{ \longrightarrow}  compliment angles.
\mathrm{Case\: I \quad t_1=\frac{2 u \sin \theta}{g} \: \, \: \, Case \ II \quad \, } \mathrm{ t_2=\frac{2 u \sin \left(90^{\circ}-\theta\right)}{g}=\frac{2 u \cos \theta}{g}}
Now, Product of two times of flight \mathrm{t_1 \cdot t_2 } will become-
\mathrm{\begin{aligned} & t_1 \cdot t_2=\frac{4 u^2 \sin \theta \cos \theta}{g^2} \\ & t_1 \cdot t_2=\frac{2}{g}\left[\frac{u^2 \sin 2 \theta}{g}\right] \end{aligned}}
\mathrm{\begin{aligned} & t_1 \cdot t_2=\frac{2 R}{g} \\ & t_1 \cdot t_2 \propto R \end{aligned}}

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manish painkra

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