Project 3: The Ballistics Computer (Trigonometry Simulator)

Build a simulator that predicts projectile motion using angles and velocity.

Project Overview

Attribute Value
Difficulty Level 1: Beginner
Time Estimate Weekend
Main Language Python
Alternative Languages JavaScript, C++
Knowledge Area Trigonometry and kinematics
Tools Plotting tool
Main Book “Physics for Scientists and Engineers” by Serway & Jewett

What you’ll build: A simulator that shows the trajectory of a projectile given initial velocity and angle.

Why it teaches math: Trig and algebra directly control real-world motion and distance.

Core challenges you’ll face:

  • Converting angle to x/y components
  • Computing flight time and range
  • Handling different initial heights

Real World Outcome

You will input an angle and velocity and see a plotted trajectory with range and maximum height.

Example Output:

$ python ballistics.py --angle 45 --speed 30
Range: 91.8 m
Max height: 22.9 m
Flight time: 4.3 s

Verification steps:

  • Compare results for 45 degrees vs other angles
  • Validate with known kinematic formulas

The Core Question You’re Answering

“How does an angle turn into a real trajectory and landing point?”

This is trigonometry in action.

Concepts You Must Understand First

Stop and research these before coding:

  1. Trig components
    • How do sine and cosine split velocity into x and y?
    • Book Reference: “Precalculus” by James Stewart, Ch. 5
  2. Projectile motion equations
    • How do you compute position over time under gravity?
    • Book Reference: “Physics for Scientists and Engineers” by Serway & Jewett, Ch. 3
  3. Range and max height
    • How do you derive formulas for range and peak?
    • Book Reference: “Physics for Scientists and Engineers” by Serway & Jewett, Ch. 3

Questions to Guide Your Design

  1. Time stepping
    • Will you compute positions analytically or via simulation steps?
    • How small should the time step be?
  2. Visualization
    • Will you plot the path or animate it?
    • How will you mark key values?

Thinking Exercise

Angle Comparison

Compute the range for angles 30, 45, and 60 degrees with the same speed. Which is longest?

Questions while working:

  • Why does 45 degrees maximize range without air resistance?
  • What changes if launch height is not zero?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “Why does 45 degrees maximize range?”
  2. “How do you decompose velocity into components?”
  3. “What assumptions does projectile motion make?”
  4. “How does launch height affect flight time?”
  5. “How would air resistance change the model?”

Hints in Layers

Hint 1: Starting Point Start with formulas for x(t) and y(t).

Hint 2: Next Level Compute when y(t) reaches zero to find flight time.

Hint 3: Technical Details Use radians for trig functions and keep units consistent.

Hint 4: Tools/Debugging Plot the trajectory and verify symmetry for zero launch height.

Books That Will Help

Topic Book Chapter
Trig components “Precalculus” by James Stewart Ch. 5
Projectile motion “Physics for Scientists and Engineers” by Serway & Jewett Ch. 3
Kinematics “Physics for Scientists and Engineers” by Serway & Jewett Ch. 3

Implementation Hints

  • Use analytic equations first, then add simulation as a check.
  • Keep gravity as a parameter for experimentation.
  • Label axes and key points on the plot.

Learning Milestones

  1. First milestone: You can compute range and max height.
  2. Second milestone: You can plot trajectories for any angle.
  3. Final milestone: You can explain why trajectories are parabolic.