Answer-A particle is projected such that its velocity vector sweeps equal angles with horizontal at equal t...

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We are told that the velocity vector sweeps equal angles with the horizontal in equal time intervals.  This implies that the direction of the velocity vector changes uniformly with time  meaning the rate of change of the direction angular change is constant.   In uniform projectile motion , the angle of velocity with horizontal does not change uniformly. It depends on vertical velocity vy  u sin  gt, which is linear in time, so angle changes non-uniformly.   Non-uniform projectile with variable g could produce some complex motion, but it wouldnt necessarily cause a uniform angular sweep of the velocity vector unless fine-tuned, which is unlikely here.  In spiral motion , both magnitude and direction of velocity change in a way that creates spiraling paths  but again, the velocity vector does not sweep equal angles in equal time generally.  In uniform circular motion , the velocity vector changes direction at a constant angular rate while maintaining constant speed. This perfectly matches the condition  the velocity vector sweeps equal angles in equal time.

A particle is projected such that its velocity vector sweeps equal angles with horizontal at equal time intervals. The motion is best described as:

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