# Projectile Motion: Understanding Dynamics in Two-Dimensions

## What happens to the velocity and acceleration of a projectile at its apex in the absence of air resistance?

Choose the correct statement regarding projectile motion in the absence of air resistance. Assume the object is at sea level moving from left.

### Final answer:

For a projectile at its apex in the absence of air **resistance**, the vertical (y) velocity is zero and acceleration is negative due to gravity. There is no change in horizontal (x) velocity and hence, its acceleration remains zero. The analysis of two-dimensional motion - into vertical and horizontal motions - is key to understanding these dynamics.

### Explanation:

In terms of **projectile **motion in the absence of air resistance, the correct statement would be that at the apex, in the y direction, the velocity is zero and the acceleration is negative due to **gravity**. However, in the x direction at the apex, the velocity remains constant and the acceleration is zero because there are no forces acting horizontally.

Two-dimensional projectile motion can be broken down into two independent **one-dimensional **motions. One of these is in the vertical (y) direction under the influence of gravity, and the other is in the horizontal (x) direction, where velocity stays constant in the absence of air resistance. The **x-component **of a projectile's acceleration is zero because the acceleration of a projectile is purely due to gravity, which acts vertically or in the y direction. Therefore, at the apex of the motion, the vertical velocity will be zero as the object temporarily stops before falling back down due to gravity.

Understanding these aspects of two-dimensional motion are crucial to analyzing scenarios involving projectile motion and can be applied to various real-world situations, like calculating trajectories in sports or anticipating the impact location of a falling object.