Final answer:
In projectile motion, gravity only affects the vertical motion, so the x-component of the acceleration is 0 and the horizontal velocity remains constant. This is because horizontal and vertical motions are independent of each other.
Step-by-step explanation:
The reason we do not add acceleration due to gravity to the horizontal motion formula in projectile motion is that gravity only affects the vertical component of the motion. In projectile motion, we separate the movement into two independent one-dimensional motions along the vertical and horizontal axes. Since the only force acting on the projectile is gravity, which pulls it down toward the Earth, there is no horizontal acceleration, and hence the x-component of the acceleration (ax) is 0. This means the horizontal velocity (vx) remains constant throughout the motion, assuming no air resistance.
Furthermore, the independence of horizontal and vertical motions is a fundamental concept in projectile motion, helping us understand that while an object is affected by gravity in the vertical direction, its horizontal motion continues at a steady rate. To recap:
- Horizontal motion: ax = 0, constant horizontal velocity (vx).
- Vertical motion: ay = g (acceleration due to gravity), which affects vertical velocity (vy).