A projectile of mass ' \( m \) ' has a velocity \( v_{1} \) at a certain instant of time and a velocity \( \overrightarrow{v_{2}} \) after some time. If \( \vec{v}_{1} \perp \vec{v}_{2} \), then minimum kinetic energy of the projectile during its flight is (1) \( \frac{m\left(v_{1}^{3}+v_{2}^{3}\right)}{2 \sqrt{v_{1} v_{2}}} \) (2) \( \frac{m v_{1}^{2} v_{2}^{2}}{2\left(v_{1}^{2}+v_{2}^{2}\right)} \) (3) \( \frac{m v_{1}^{2}}{2} \) (4) \( \frac{m v_{1} v_{2}}{2} \)

Question

A projectile of mass ' \( m \) ' has a velocity \( v_{1} \) at a certain instant of time and a velocity \( \overrightarrow{v_{2}} \) after some time. If \( \vec{v}_{1} \perp \vec{v}_{2} \), then minimum kinetic energy of the projectile during its flight is (1) \( \frac{m\left(v_{1}^{3}+v_{2}^{3}\right)}{2 \sqrt{v_{1} v_{2}}} \) (2) \( \frac{m v_{1}^{2} v_{2}^{2}}{2\left(v_{1}^{2}+v_{2}^{2}\right)} \) (3) \( \frac{m v_{1}^{2}}{2} \) (4) \( \frac{m v_{1} v_{2}}{2} \)