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Angled Projectile Motion Explorer

Run the Angled Projectile MicroSim Fullscreen

Description

This MicroSim allows you to explore the full range of projectile motion by adjusting launch angle, initial speed, and launch height. Watch how these parameters affect the trajectory, maximum height reached, horizontal range, and flight time. The simulation includes special features like complementary angle comparison and trajectory overlay.

Key Concepts

  • Initial Velocity Components:
    • \(v_{0x} = v_0 \cos\theta\) (horizontal, constant)
    • \(v_{0y} = v_0 \sin\theta\) (vertical, changes with time)
  • Maximum Height: \(y_{max} = y_0 + \frac{v_{0y}^2}{2g}\)
  • Range (from ground level): \(R = \frac{v_0^2 \sin(2\theta)}{g}\)
  • 45-degree rule: Maximum range occurs at 45 degrees (on level ground)
  • Complementary angles: 30 and 60 degrees produce the same range

How to Use

  1. Adjust Angle (5-85 degrees) to change launch direction
  2. Adjust Speed (5-40 m/s) to change initial velocity
  3. Adjust Height (0-20 m) to launch from an elevated platform
  4. Click Launch to fire the projectile
  5. Enable Complementary Angle to simultaneously launch at the complementary angle (90 - angle)
  6. Enable Keep Trails to overlay multiple trajectories for comparison
  7. Enable Velocity Components to see horizontal and vertical velocity vectors

Learning Objectives

After using this MicroSim, students should be able to:

  1. Decompose initial velocity into horizontal and vertical components
  2. Explain why 45 degrees gives maximum range on level ground
  3. Understand that complementary angles produce equal ranges
  4. Calculate maximum height from initial vertical velocity
  5. Predict how changing angle affects height vs. range tradeoff