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3.2 , motion in plane — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
Two stones are thrown with same speed $u$ at different angles from ground in air. If both stones have same range and height attained by them are $h_1$ and $h_2$, then $h_1+h_2$ is equal to .......
  • A
    $\frac{u^2}{g}$
  • ✓
    $\frac{u^2}{2 g}$
  • C
    $\frac{u^2}{3 g}$
  • D
    $\frac{u^2}{4 g}$
✓

Answer

Correct option: B.
$\frac{u^2}{2 g}$
b
(b)

If range is same then, one angle is $\theta$ and other angle is $(90-\theta)$

$\Rightarrow h_1=\frac{u^2 \sin ^2 \theta}{2 g}, h_2=\frac{u^2 \sin ^2(90-\theta)}{2 g}$

$h_1=\frac{u^2 \sin ^2 \theta}{2 g}, h_2=\frac{u^2 \cos ^2 \theta}{2 g}$

So, $h_1+h_2 \Rightarrow \frac{u^2 \sin ^2 \theta}{2 g}+\frac{u^2 \cos ^2 \theta}{2 g}=\frac{u^2}{2 g}\left(\sin ^2 \theta+\cos ^2 \theta\right)$

$h_1+h_2=\frac{u^2}{2 g}$

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