Projectile Motion Calculator

The Projectile Motion Calculator solves the classic two-dimensional kinematics problem. Given an initial velocity and launch angle (and optional initial height), it computes horizontal range, maximum height, time of flight, and final velocity components. Ideal for physics students, engineers, and anyone studying ballistic trajectories under constant gravity.

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rocket_launch Launch Parameters

45°
45° (max range)90°

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Range
meters
Max Height
meters
Time of Flight
seconds
Final Speed
m/s

Velocity Components

Horizontal vₓ
Vertical v_y₀
Time to apex
Optimal angle

Trajectory

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lightbulb Tips

  • 45° gives maximum range on flat ground
  • Horizontal velocity is constant throughout
  • Max height reached at T/2 of flight time
  • Moon gravity (1.62): range is ~6× Earth

rocket_launch Key Formulas

Range R vₓ × T
Max Height H vy²/(2g)
Flight Time T 2vy/g
Gravity by Planet
Earth 9.81 m/s²
Moon 1.62 m/s²
Mars 3.72 m/s²
Jupiter 24.79 m/s²

The Formula

Horizontal and vertical motion are independent. Horizontal: x = v₀cos(θ)·t. Vertical: y = v₀sin(θ)·t − ½g·t²

R = v₀²sin(2θ)/g | H = v₀²sin²(θ)/(2g) | T = 2v₀sin(θ)/g

lightbulb Variables Explained

tips_and_updates Pro Tips

1

45° launch angle maximizes range on flat ground

2

Maximum height is reached at T/2 (halfway through flight)

3

Horizontal velocity is constant — only vertical is affected by gravity

4

On the Moon (g=1.62 m/s²) range is ~6× greater than on Earth

5

Adding initial height increases both range and time of flight

Frequently Asked Questions

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Data sourced from trusted institutions

All formulas verified against official standards.