The last four lessons told two separate stories about one flying ball. Sideways: a velocity that never changes, because no horizontal force acts. Straight down: free fall, because gravity acts straight down. Two one-direction stories, and neither one ever mentioned the other.
This lesson names the idea that lets both stories run at once.
The horizontal story never needed the fall. The vertical story never needed the sideways speed.
The reason: because perpendicular components of motion do not affect each other, each direction can be analyzed as its own one-dimensional motion.
What is true of a projectile's horizontal and vertical motions?
So a projectile problem splits into two problems you already know how to solve: a constant-velocity problem sideways, and a free-fall problem downward.
A golf ball's flight is treated as a projectile problem. Into which two problems does it split?
Each problem runs on its own numbers. Nothing from one direction enters the other.
A paintball is fired horizontally over a field. Name the two one-dimensional problems its flight splits into.
The horizontal and vertical motions are independent, so take one direction at a time.
Sideways, the horizontal velocity stays constant: a constant-velocity problem.
Downward, the motion is free fall: a free-fall problem.
A constant-velocity problem sideways and a free-fall problem downward.
Mid-flight, a soccer ball's downward speed doubles. What happens to its horizontal velocity?
The river crossing used the same idea: the current, perpendicular to the crossing motion, could not change the crossing time. The projectile brings the same independence to a new perpendicular pair: sideways motion and falling motion.
Which statement about a projectile's two motions is true?
A rock is knocked horizontally off a ledge. Which pair of problems does its flight split into?
The vertical motion of a thrown ball is analyzed on its own, as a one-dimensional problem. What makes this legal?