No, Vy and Uy in projectile motion are not the same. They represent different components of the initial velocity of a projectile.
In projectile motion, an object is launched into the air and moves along a curved trajectory under the influence of gravity. The initial velocity of the projectile can be broken down into two components: the horizontal component (Ux) and the vertical component (Uy).
Ux represents the initial velocity in the horizontal direction. It remains constant throughout the motion since there are no horizontal forces acting on the projectile (assuming no air resistance). The horizontal component does not change the height of the projectile, only its horizontal displacement.
Uy represents the initial velocity in the vertical direction. It determines the initial height and the vertical motion of the projectile. As the projectile moves, the vertical component changes due to the influence of gravity, causing the object to accelerate downward. The vertical component decreases until reaching its highest point (where Uy becomes zero) and then increases as the object falls back down.
So, while Uy represents the initial vertical velocity of the projectile, Vy refers to the instantaneous vertical velocity at any given point during the projectile's motion. Vy changes continuously due to the effect of gravity, whereas Uy remains constant throughout the motion unless the initial velocity is changed.