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3-2.Motion in Plane
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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$\frac{u^2}{g}$
B$\frac{u^2}{2 g}$
C$\frac{u^2}{3 g}$
D$\frac{u^2}{4 g}$
Solution
(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, $h_1+h_2 \Rightarrow \frac{u^2 \sin ^2 \theta}{2 g}+\frac{u^2 \cos ^2 \theta}{2 g}=\frac{u^2}{2 g}\left(\sin ^2 \theta+\cos ^2 \theta\right)$
$h_1+h_2=\frac{u^2}{2 g}$
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, $h_1+h_2 \Rightarrow \frac{u^2 \sin ^2 \theta}{2 g}+\frac{u^2 \cos ^2 \theta}{2 g}=\frac{u^2}{2 g}\left(\sin ^2 \theta+\cos ^2 \theta\right)$
$h_1+h_2=\frac{u^2}{2 g}$
Standard 11
Physics
