A projectile thrown from ground at some angle is having velocities $\vec{u}$ and $\vec{v}$ at two points during its flight. If $\vec{u}$ and $\vec{v}$ are perpendicular to each other then the minimum kinetic energy of projectile during the journey is (mass of the projectiles is m)

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$\frac{1}{2} m (\frac{u^{2} v^{2}}{u^{2} + v^{2}})$

$\frac{1}{2} m (\frac{u^{2} v^{2}}{u^{2} - v^{2}})$

$\frac{m}{4} \frac{u^{2} v^{2}}{(u^{2} - v^{2})}$

$\frac{m}{4} \frac{u^{2} v^{2}}{(u^{2} + v^{2})}$

answer is A.

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Detailed Solution

$u \cos α = v \cos β u \cos α = v \sin α [α + β = 90 °]$

$K . E_{\min} = \frac{1}{2} m u^{2} \cos^{2} α$

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