Projectile Motion Experiment Calculator

Analyze projectile trajectories and design physics experiments

Calculation Mode

Calculate trajectory from initial conditions

Launch Parameters

degrees

Example Experiment

Rubber Ball Launch

Launcher: Resistance band and chair

Launch height: 1.2 meters

Time of flight: 1.5 seconds

Horizontal distance: 4.8 meters

Calculated Results

Initial velocity: 8.2 m/s

Launch angle: 35.6°

Maximum height: 2.4 meters

Perfect for classroom demonstration!

Key Equations

Velocity Components

Vₓ = V cos(α)
Vᵧ = V sin(α)

Time of Flight

t = [Vᵧ + √(Vᵧ² + 2gh)] / g

Range

R = Vₓ × t

Maximum Height

h_max = h + Vᵧ² / (2g)

Experiment Materials

Launcher

  • • Resistance band
  • • Four-legged chair
  • • Rubber ball

Measurement

  • • Measuring tape
  • • Stopwatch
  • • Masking tape
  • • Marker

Safety

  • • Safety goggles
  • • Clear pathway
  • • Alert others nearby

Physics Tips

45° gives maximum range on level ground

Air resistance ignored for simplicity

Consistent launches improve accuracy

Video recording helps timing

⚠️

Never aim at people or breakables

Understanding Projectile Motion

What is Projectile Motion?

Projectile motion occurs when an object is launched into the air and moves under the influence of gravity alone. The object follows a parabolic trajectory, with horizontal and vertical components of motion that are independent of each other.

Key Principles

  • Horizontal velocity remains constant (no air resistance)
  • Vertical acceleration is constant (-9.81 m/s²)
  • Motion is symmetric about the highest point
  • Independent horizontal and vertical components

Experiment Design

Forward Calculation

Use known launch parameters (velocity, angle, height) to predict the trajectory, range, time of flight, and maximum height.

Experiment Analysis

Measure time of flight, horizontal distance, and launch height to calculate the initial velocity and launch angle of your projectile.

Safety First: Always wear eye protection and ensure the launch area is clear of people and breakable objects.

Historical Context

Galileo Galilei was the first to accurately describe projectile motion in the early 1600s. He realized that projectile motion could be understood by analyzing horizontal and vertical components separately. His experiments with bronze balls led to the discovery that all projectiles follow parabolic paths when air resistance is negligible.

Real-World Applications

Sports & Recreation

  • • Basketball shot trajectories
  • • Baseball and golf ball paths
  • • Javelin and shot put analysis
  • • Archery and target shooting

Engineering & Science

  • • Artillery and ballistics
  • • Satellite orbital mechanics
  • • Water fountain design
  • • Package delivery drones