🎓 Physics • Motion
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Projectile Motion Calculator
Interactive 2D kinematics projectile motion solver. Plots parabolic trajectory, calculates maximum height, flight time, and range.
🎯 2D Projectile Motion Ballistic Simulator
Computes parabolic flight trajectory, apex altitude, airtime, and horizontal range under uniform gravity.
● Apex: 15.93 m (at t = 1.8s)2D Parabolic Ballistic Trajectory● Range: 63.73 m
Horizontal Range (R)63.73 mDistance covered
Maximum Height (H)15.93 mPeak altitude
Total Flight Time (T)3.61 sAirtime duration
Impact Speed25 m/sat 45°
📐 Vector Components & Step-by-Step Derivation
Horizontal Velocity (Constant): v_{0x} = v₀ cos θ25 × cos(45°) = 17.68 m/s
Initial Vertical Velocity: v_{0y} = v₀ sin θ25 × sin(45°) = 17.68 m/s
• Time to Apex: t_{peak} = v_{0y} / g = 17.68 / 9.80665 = 1.8 s
• Max Altitude: H = h₀ + v_{0y}² / (2g) = 0 + (17.68)² / (2 × 9.80665) = 15.93 m
• Flight Time: t_{flight} = (v_{0y} + √(v_{0y}² + 2gh₀)) / g = 3.61 s
• Total Range: R = v_{0x} × t_{flight} = 17.68 × 3.61 = 63.73 m
What is Projectile Motion?
Projectile motion describes the motion of an object launched into the air subject only to the downward pull of gravity.
The horizontal motion continues at constant velocity while the vertical motion experiences constant gravitational acceleration.
Formula & Step-by-Step Calculation
R = (v₀² · sin(2θ)) / g, H = (v₀² · sin²(θ)) / (2g)
Horizontal range and maximum apogee height for ground launches.
Worked Step-by-Step Examples
Example 1
Launch speed 25 m/s at 45° on Earth
Solution: Range = 63.73 m, Max Height = 15.93 m
• R = (25² × sin 90°) / 9.81 = 625 / 9.81 ≈ 63.73 m
Common Real-World & Academic Use Cases
- ✓ Ballistics and artillery trajectory modeling
- ✓ Sports biomechanics (golf, basketball, soccer)
- ✓ Firefighting water hose angle projection
How to Use the Projectile Motion Calculator
1
Set Launch Speed & Angle
Enter initial speed v₀ and angle θ.
2
Inspect Plot
Review apex, range, and flight duration on the canvas graph.
Frequently Asked Questions
Q: What angle gives maximum range in a vacuum?
45 degrees produces the maximum horizontal range on level ground.