This animation compares the motions of a horizontally projected body and a dropped body. You should be able to notice that their vertical components of motion are identical.

In other words adding a horizontal component of velocity to the motion does not affect the vertical component of motion. They are independent of each other. This could be the key to the understanding of projectile motion and is reflected in the writing of equations of motion for any two mutually perpendicular directions.

In other words adding a horizontal component of velocity to the motion does not affect the vertical component of motion. They are independent of each other. This could be the key to the understanding of projectile motion and is reflected in the writing of equations of motion for any two mutually perpendicular directions.