Question
Two particles are projected from the same point with the same speed $u$ such that they have the same range $R,$ but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?
✓
Answer
For same range angle of projection will
be $\theta $ will be $\theta ,90 - \theta$
$R\,\, = \,\frac{{{u^2}2\sin \theta \cos \theta }}{g}$
${h_1} = \frac{{{u^2}{{\sin }^2}\theta }}{g}$
${h_2} = \frac{{{u^2}\sin {\,^2}\left( {90 - \theta } \right)}}{g}$
$\frac{{{R^2}}}{{{h_1}{h_2}}} = 16 $
be $\theta $ will be $\theta ,90 - \theta$
$R\,\, = \,\frac{{{u^2}2\sin \theta \cos \theta }}{g}$
${h_1} = \frac{{{u^2}{{\sin }^2}\theta }}{g}$
${h_2} = \frac{{{u^2}\sin {\,^2}\left( {90 - \theta } \right)}}{g}$
$\frac{{{R^2}}}{{{h_1}{h_2}}} = 16 $
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