The Memory Trick
💡 Horizontal and Vertical Are Independent
Projectile motion is the combination of two entirely independent motions happening simultaneously: constant horizontal velocity (ignoring air resistance) and vertically accelerating motion due to gravity (9.8 m/s² downward). Neither motion affects the other.
Why It Works
Because gravity only acts vertically, it never changes the horizontal velocity — and because there's no horizontal force (ignoring air resistance), horizontal velocity never changes anything about the vertical fall. Treating them as two separate, simpler problems is what makes projectile motion tractable.
Step by Step
Solving Projectile Motion Problems
1
Split the initial velocity into components
Any launch angle θ produces horizontal component vₓ = v·cos θ and vertical component vy = v·sin θ — solve each independently from there.
A ball launched at 20 m/s at 30° has vₓ = 20cos30° ≈ 17.3 m/s and vy = 20sin30° = 10 m/s.
2
Horizontal velocity never changes
With no horizontal force, vₓ stays exactly the same from launch to landing — this constant value is what you use to find range (horizontal distance).
If vₓ = 17.3 m/s, the projectile still has vₓ = 17.3 m/s the instant before it lands, having never accelerated horizontally.
3
Vertical velocity follows constant acceleration
At the peak of the trajectory, vertical velocity is exactly zero (momentarily) — the projectile is still moving horizontally the whole time, just not vertically at that instant.
Using the range formula R = v²sin(2θ)/g, maximum range for a given launch speed always occurs at a 45° launch angle.
🏥 Worked Example
A projectile is launched at 25 m/s at an angle of 40° above horizontal. What is its horizontal range (assume it lands at the same height it launched from)?
1
Apply the range formula: R = v²sin(2θ)/g.
2
Plug in values: R = (25²) × sin(80°) / 9.8 = 625 × 0.985 / 9.8 ≈ 62.8 m.
3
Note: this same 25 m/s launched instead at 45° would travel slightly farther, since 45° maximizes range for any given launch speed.
📌 Exam Application
Exams test correctly splitting initial velocity into horizontal and vertical components, applying constant-velocity equations horizontally and constant-acceleration equations vertically, and knowing that maximum range occurs at 45°.
⚠️ Most Common Projectile Motion Mistakes
The most common trap is trying to apply a single combined equation to the whole trajectory at once, instead of treating horizontal and vertical motion as two separate, independent problems that only share a common time variable.
✓ Quick Self-Test
1) What two types of motion combine to create projectile motion, and are they dependent on each other? Constant horizontal velocity and constantly accelerating vertical motion (due to gravity) — they are completely independent of each other. 2) What is the vertical velocity of a projectile at the peak of its trajectory? Zero, momentarily. 3) Does horizontal velocity change at any point during projectile motion (ignoring air resistance)? No — it stays constant throughout the entire flight. 4) At what launch angle is horizontal range maximized for a given launch speed? 45°. 5) Write the range formula for projectile motion (assuming equal launch and landing height). R = v²sin(2θ)/g.