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Projectile motion is a combination of two one-dimensional motions: one in horizontal and other in vertical direction. Motion in \( 2 D \) means in a plane. Necessary condition for \( 2 D \) motion is that the velocity vector is coplanar to the acceleration vector. In case of projectile motion, the angle between velocity and acceleration will be \( 0^{\circ}\theta180^{\circ} \). During the projectile motion, the horizontal component of velocity remains unchanged but vertical component of velocity is time dependent. Now answer the following questions:
A particle is projected from the origin in the \( x-y \) plane. The acceleration of particle in negative \( y \)-direction is \( \alpha \). If equation of path of the particle is \( y=a x-b x^{2} \), then initial velocity of the particle is
(1) \( \sqrt{\frac{\alpha}{2 b}} \)
(2) \( \sqrt{\frac{\alpha\left(1+a^{2}\right)}{2 b}} \)
(3) \( \sqrt{\frac{\alpha}{a^{2}}} \)
(4) \( \sqrt{\frac{\alpha b}{a^{2}}} \)
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