Projectile components are independent only after forces are split

01
The tempting model
Letting horizontal velocity affect vertical acceleration in ideal projectile motion.
02
Why it feels right
A faster throw clearly changes the path, so it feels like it changes every component.
03
Where it breaks · how to catch it
You put horizontal speed into the vertical acceleration equation with no horizontal force.
04
The correct model
With only gravity, a_x = 0 and a_y = -g. Horizontal and vertical motions share time but have separate kinematic equations.
05
Repair · see it, then test it
worked example A ball is launched horizontally from a table. What is its vertical acceleration just after launch?
Tempting move
Less than g because it is moving sideways.
Correct move
g downward; horizontal velocity does not change vertical acceleration.
Test the repair NL-19 · transfer

Two balls leave the same height simultaneously, one dropped and one launched horizontally. Neglect drag. Which lands first?
The dropped ball The launched ball They land together It depends on horizontal launch speed

Make a fresh prediction before referring to the worked example.
Then practise it on the ladder
R15Projectile componentsadds: Horizontal velocity and vertical acceleration are independent when only gravity acts.