Topic 08: Projectile Trajectories — Physics Universe

🎯 PROJECTILE TRAJECTORIES

TOPIC 08 · PHYSICS · GRAVITY · PARABOLAS · FLIGHT

PAGE 1 OF 5, TWO MOTIONS AT ONCE

THE BIG IDEA

HORIZONTAL AND VERTICAL MOTION ARE INDEPENDENT

Throw a ball, kick a football, or shoot a basketball and you launch a projectile. The moment it leaves your hand or foot, two separate stories begin. Horizontally, the object keeps the speed you gave it (ignoring air). Vertically, gravity pulls it down at 9.8 m/s², the same acceleration for every object on Earth. These two motions do not interfere with each other. That independence is the secret behind every parabolic arc you see in sport and nature.

⚡ DID YOU KNOW?

A bullet fired horizontally and a bullet dropped from the same height hit the ground at the same time (in a vacuum). Horizontal speed does not slow the fall!

SPLIT!

HORIZONTAL

➡️ v_x stays constant (no air)
→ Distance = speed × time
⚽ Kick harder = more horizontal speed

VERTICAL

⬇️ Gravity: g = 9.8 m/s² downward
⬆️ Upward speed slows, then reverses
🏀 Same g for every mass

PAGE 2 OF 5, THE PARABOLIC PATH

NATURE'S FAVOURITE CURVE

EVERY PROJECTILE TRACES A PARABOLA

Combine steady horizontal motion with constant downward acceleration and you get a parabola, a symmetric U-shaped curve. At the peak, vertical velocity is zero but horizontal velocity is unchanged. On the way down, vertical speed increases again while horizontal speed stays the same. Water from a fountain, a cricket ball in the air, and a long pass in football all follow this same mathematical shape. Galileo was among the first to recognise that projectile paths are parabolic when air resistance is small.

ARC!

📐 PEAK HEIGHT

⬆️ Higher launch angle = higher peak
→ Steeper shot climbs further
🏀 Depends on initial vertical speed

⏱️ TIME OF FLIGHT

⏱️ Upward & downward times match
→ Symmetric path (no air)
🎯 More vertical speed = longer air time

🌊 FOUNTAIN ARC

💧 Water streams = tiny projectiles
→ Each drop follows a parabola
🎆 Fireworks use the same physics

PAGE 3 OF 5, LAUNCH ANGLE & RANGE

45° ANGLE

Comic illustration: LAUNCH ANGLE AND RANGE, 45 DEGREE ANGLE

📐 45° gives max range on flat ground
→ Equal horizontal & vertical parts
⚽ Ideal for long passes (no air drag)

STEEP vs FLAT

🎯 High angle = short range, high peak
➡️ Low angle = long skim, low peak
🏀 Shooters pick angle for the hoop

RANGE EQUATION

HOW FAR WILL IT FLY?

Range is how far a projectile travels horizontally before landing at the same height it started. On level ground with no air resistance, range depends on launch speed, launch angle, and gravity. Double the launch speed and the range quadruples. Launch at complementary angles (like 30° and 60°) from the same speed and you get the same range. Football free kicks, rugby conversions, and javelin throws all balance speed and angle to maximise distance or accuracy.

📐 RANGE (LEVEL GROUND, NO AIR)

R = v² sin(2θ) / g, where v is launch speed, θ is launch angle, and g = 9.8 m/s²

RANGE!

PAGE 4 OF 5, GRAVITY & REAL-WORLD FLIGHT

g = 9.8 m/s²

Comic illustration: GRAVITY AND REAL-WORLD FLIGHT, g equals 9.8 metres per second squared

GRAVITY PULLS EVERY PROJECTILE DOWNWARD

Every second an object is in the air, gravity increases its downward speed by 9.8 metres per second. After one second of free fall, vertical speed is 9.8 m/s downward. After two seconds, 19.6 m/s, and so on. This constant acceleration is why projectiles curve so predictably. On the Moon, where g is about 1.6 m/s², a golf ball would fly six times farther for the same kick. On Jupiter's surface, g is roughly 24.8 m/s², so throws would fall much faster and land much closer.

GRAVITY!

⚽ FOOTBALL

⚽ Curved free kicks use spin + air
→ Magnus effect bends the path
🥅 Goalkeepers read the parabola

🏀 BASKETBALL

🏀 Arc shot = higher entry angle
→ Softer bounce off the rim
📐 Coaches teach optimal launch angle

💨 AIR RESISTANCE

💨 Drag slows horizontal motion
→ Real paths are not perfect parabolas
🪶 Feather vs ball: air matters hugely

PAGE 5 OF 5, MASTER THE TRAJECTORY

PREDICT THE PATH

PHYSICS BEHIND EVERY THROW

Once you understand projectile motion, the flight of any ball becomes readable. Split the motion into horizontal and vertical parts, apply g = 9.8 m/s² to the vertical side, and the full path appears. Engineers use these same equations for artillery, rocket stages, and satellite launches. Athletes use them instinctively when they adjust power and angle. The parabola is not just a maths shape. It is the signature of gravity acting on anything that flies through the air.

🎯 KEY EQUATIONS

x = v_x × t, y = v_yt − ½gt², g = 9.8 m/s² on Earth

FLIGHT!

🎯 SPORTS SCIENCE

📊 TrackMan & Hawk-Eye map trajectories
→ Data guides training & tactics
⚽ Optimal angles vary with air & spin

REMEMBER

🎯 KEY FACTS

Horizontal and vertical motion are independent. Combined path is a parabola. g = 9.8 m/s² on Earth. 45° gives maximum range on flat ground (no air). Range grows with the square of launch speed.

✅ Split motion into x and y
✅ Gravity only affects vertical
✅ Parabola = constant g + steady v_x
✅ Air drag changes real-world paths

🧠 QUIZ TIME!

PROJECTILE TRAJECTORIES · 5 QUESTIONS

QUESTION 01

In projectile motion (ignoring air resistance), what happens to horizontal velocity after launch?

QUESTION 02

What shape does the path of a projectile follow (with no air resistance)?

QUESTION 03

What is the value of gravitational acceleration g on Earth's surface (approximately)?

QUESTION 04

On level ground with no air resistance, which launch angle gives the maximum range for a fixed speed?

QUESTION 05

At the highest point of a projectile's path, what is true about its velocity?

0/5

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