Projectile Motion Calculator
Simple Mode
Advanced Mode
m/s
deg
m
m/s²
Calculates Drag Force: \(F_d = \frac{1}{2} \rho C_d A v^2\)
kg
(Sphere ≈ 0.47)
m²
kg/m³
m/s
Total Time
—
Max Height
—
Max Range
—
0.0s
Current State (t):
Vx: 0 m/s |
Vy: 0 m/s |
Height: 0 m
Calculation Logic:
Using standard kinematic equations (Vacuum).
Using standard kinematic equations (Vacuum).
Understanding Projectile Motion
Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth’s surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are assumed to be negligible).
Physics Formulas Used (Simple Mode)
- Horizontal Distance (x): \( x = v_0 \cdot \cos(\theta) \cdot t \)
- Vertical Position (y): \( y = h_0 + v_0 \cdot \sin(\theta) \cdot t – \frac{1}{2}gt^2 \)
- Time to Max Height: \( t_{peak} = \frac{v_0 \cdot \sin(\theta)}{g} \)
Frequently Asked Questions (FAQ)
Q: Why does 45 degrees give the max range?
A: Mathematically, \(\sin(2\theta)\) is maximized when \(2\theta = 90^\circ\), meaning \(\theta = 45^\circ\). This assumes launch and landing heights are equal.
Q: How does air resistance affect the projectile?
A: Air resistance (drag) opposes the direction of motion. It reduces both the maximum height and the total range, and makes the trajectory asymmetrical (the descent is steeper than the ascent).