Projectile Motion

Mechanics module exploring motion under constant gravitational acceleration.

Learning objectives

• Resolve velocity into horizontal and vertical components.
• Explain why projectile paths are parabolic.
• Calculate flight time, maximum height, and range.
• Interpret the effect of gravity on motion.

First principles

Projectile motion combines constant horizontal velocity with vertically accelerated motion caused by gravity.

Core equations

• uₓ = u cosθ
• uᵧ = u sinθ
• t = 2uᵧ/g
• R = u²sin(2θ)/g
• h = uᵧ²/(2g)

Worked example

A projectile is launched at 20 m/s and 45°. Estimate its range on Earth (g = 9.81 m/s²).

Interactive simulator

Launch locally on port 8502.

streamlit run simulations/projectile_motion/streamlit_projectile_app.py

Engineering meaning

Projectile motion appears in ballistics, robotics, sports engineering, aerospace systems, and autonomous targeting systems.

Challenge questions

1. Why does 45° maximise range under ideal conditions?
2. How does lunar gravity affect flight time?
3. What assumptions fail when air resistance becomes important?

HeliosSTEMLab · Phase 2A learner module