Projectile motion is a combination of two one-dimensional motions: one in horizontal and other i...

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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:

An object is projected from origin in \( x-y \) plane in which velocity changes according to relation \( \vec{v}=a \breve{i}+b x \breve{j} \). Path of particle is
(1) Hyperbolic
(2) Circular
(3) Elliptical
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