Projectile motion is a combination of two one-dimensional motion: one in horizontal and other in vertical direction. Motion in 2D means in a plane. Necessary condition for 2D 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^@`lt`theta`lt`180^@`. During the projectile motion, the horizontal component of velocity ramains unchanged but the 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 `vecv = a hati + bx hatj`. Path of particle is

Options

A. Hyperbolic
B. Circular
C. Elliptical
D. parabolic

Answer

D

Explanation

d. `vecv = ahati + bxhatj , v_x = a or dx = adt rArr x = at`
`v_y = bx = bat or y = (bat^2)/2`
`rArr y = (ba)/2(x/a)^2 rArr y prop x^2 rarr parabolic`