Projectile Motion Simulator
Classroom worksheet · Interactive simulation: https://lkforge.com/tools/physics/projectile-motion/
Name: Date:
Learning objectives
- Explain why horizontal and vertical motion are independent.
- Predict how launch angle affects range and maximum height.
- Identify the angle that maximizes range with no air resistance.
Variables to change
- Launch angle
- Launch speed
- Gravity
- Air resistance (on/off)
Procedure
- Set gravity to Earth (9.8 m/s²) and turn air resistance off.
- Fix the launch speed. Fire at 15°, 30°, 45°, 60°, and 75°, recording the range each time.
- Fire at 30° and 60° with the same speed and compare the two ranges.
- Now turn air resistance on and repeat the 45° launch.
Observations
Record range, maximum height, and flight time for each launch angle in a table.
Questions
- Which launch angle gave the greatest range with air resistance off?
- How did the ranges at 30° and 60° compare? Why?
- Does the projectile’s mass change its trajectory (air resistance off)? Explain.
- What happened to the range and the best angle when you turned air resistance on?
- At the top of the arc, what is the vertical velocity? The horizontal velocity?
Answer key (instructors)
- 1. 45° gives the maximum range when launched and landing at the same height with no air resistance.
- 2. They are equal. Complementary angles (adding to 90°) give the same range because the range formula depends on sin(2θ), and sin(60°)=sin(120°).
- 3. No. In a vacuum all masses fall with the same acceleration g, so the path depends only on launch speed and angle, not mass.
- 4. Range decreased and the angle giving maximum range dropped below 45°, because drag removes energy and grows with speed.
- 5. Vertical velocity is zero at the peak; horizontal velocity stays constant throughout (air resistance off).
A projectile moves under gravity alone once launched. Horizontal velocity is constant while vertical velocity changes at g, so the path is a parabola. With no air resistance, 45° maximizes range and complementary angles share ranges. Air resistance shortens the range and lowers the optimal angle.