Projectile Motion Simulator
Launch a projectile and watch its trajectory in real time. Adjust the angle, initial velocity, and gravity to explore range, maximum height, and time of flight.
Launch Parameters
Properties
| Angle | 45° |
| V₀ | 25 m/s |
| V₀ₓ | -- |
| V₀ᵧ | -- |
| Max Height | -- |
| Range | -- |
| Time of Flight | -- |
| Current t | -- |
The Physics Behind It
Kinematics Formulas
- Range: R = V₀² sin(2θ) / g
- Max Height: H = V₀² sin²(θ) / (2g)
- Time of Flight: T = 2V₀ sin(θ) / g
- Horizontal position: x(t) = V₀ cos(θ) · t
- Vertical position: y(t) = V₀ sin(θ) · t − ½g t²
Key Concepts
- Independence of axes: horizontal and vertical motions are independent — gravity only affects the vertical component
- 45° maximises range on level ground because sin(2θ) peaks at θ = 45°
- Complementary angles (e.g. 30° and 60°) give the same range but different max heights and flight times
- Air resistance is neglected here — real trajectories are asymmetric and shorter
- Gravity varies across celestial bodies, dramatically changing trajectory shape
You're crushing it!