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STD 11 - 3.2 , motion in plane — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 3.2 , motion in plane4 Marks
MCQ
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 ?
  • A
    $R^2 = 4 h_1h_2$
  • B
    $R^2 = 2 h_1h_2$
  • C
    $R^2 = 16 h_1h_2$
  • D
    $R^2 = h_1h_2$
✓

Answer

For same range angle of projection will be $\theta$ will be $\theta\ \&\ 90-\theta$
$R=\frac{u^2 2 \sin \theta \cos \theta}{g}$
$h_1=\frac{u^2 \sin ^2 \theta}{g}$
$h_2=\frac{u^2 \sin ^2(90-\theta)}{g}$
$\frac{R^2}{h_1 h_2}=16$

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