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3-2.Motion in Plane
medium
The velocity at the maximum height of a projectile is $\frac{\sqrt{3}}{2}$ times its initial velocity of projection $(u)$. Its range on the horizontal plane is .............
A
$\frac{\sqrt{3} u^2}{2 g}$
B
$\frac{3 u^2}{2 g}$
C
$\frac{3 u^2}{g}$
D
$\frac{u^2}{2 g}$
Solution
(a)
$u_h=u \cos \theta$
$\frac{\sqrt{3}}{2} u=u \cos \theta$
$\Rightarrow \cos \theta=\frac{\sqrt{3}}{2}$
$\theta=30^{\circ}$
$R=\frac{u^2 \sin 2 \theta}{g}$
$=\frac{u^2 \sin 60^{\circ}}{g} \Rightarrow \frac{\sqrt{3} u^2}{2 g}=R$
Standard 11
Physics
