Time of Flight Calculator
The Physics of "What Goes Up Must Come Down"
Whether you are kicking a soccer ball, firing a cannon, or spraying water from a hose, everything on Earth follows the rules of Projectile Motion.
When an object is launched into the air, two forces act upon it:
- Gravity: Pulls it down (Vertical).
- Inertia/Velocity: Pushes it forward (Horizontal).
The "Time of Flight" is strictly determined by gravity. Interestingly, the horizontal speed does not affect how long the object stays in the air—only the vertical speed and angle matter.
Visualizing the Arc (The Parabola)
The path of any projectile creates a shape called a Parabola. The object rises, slows to a stop at the peak, and accelerates downwards.
*This arc assumes no air resistance (Physics 101 model)
The 3 Key Components
To solve any projectile problem, you must break the velocity into two parts (Vectors) using trigonometry.
1. Vertical Velocity (Vy)
This determines Height and Time. It fights against gravity.
Formula: Vy = Velocity × sin(Angle)
2. Horizontal Velocity (Vx)
This determines Range (distance). It remains constant the entire flight (ignoring air resistance).
Formula: Vx = Velocity × cos(Angle)
3. Gravity (g)
On Earth, gravity accelerates objects downwards at 9.81 m/s². If you were on the Moon, projectiles would stay in the air 6x longer because gravity is weaker.
The Golden Rule: 45 Degrees
If you want to throw a ball as far as possible, what angle should you choose?
Assuming level ground, launching at 45 degrees always results in the maximum distance.
- < 45°: It lands fast because it doesn't go high enough.
- > 45°: It goes very high (hang time) but doesn't go very far.
Real World Applications
Who actually uses this math?
| Profession | Application |
|---|---|
| Game Developers | Coding physics engines (Angry Birds is just projectile motion!). |
| Sports Analysis | Calculating the arc of a basketball shot or golf drive. |
| Forensics | Determining where a car landed after driving off an embankment. |
| Military | Artillery ballistics calculations. |