ExploreSims
ExploreSims / Physics / Mechanics / Projectile Motion
Premium experiment • real-time model

PHYSICS • MECHANICS

Projectile Motion

Launch, scrub and compare ideal trajectories. Inspect position and velocity at any instant, aim for a target, and switch gravity without leaving the experiment.

● LIVE EXPERIMENTEarth • ideal trajectory
0.00 s
Range0.00 m
Maximum height0.00 m
Flight time0.00 s
Current speed0.00 m/s
Reference range0.00 m
Target error0.00 m

Trajectory profile

height vs horizontal distance

Experiment like a physicist

Use the timeline to freeze the flight at any instant. Compare the current trajectory against a reference angle, inspect velocity components, then move the target and tune the launch until the landing error approaches zero.

Fast investigations

  1. Set Earth, 24 m/s, then compare 30°, 45° and 60°.
  2. Turn on the 60° reference and verify that complementary angles can share the same range.
  3. Scrub to the apex and watch vertical velocity approach zero while horizontal velocity stays constant.
  4. Keep the launch fixed and switch Earth → Moon → Mars to isolate gravity’s effect.

LEARN WITH THE SIMULATION

Understand Projectile Motion by experimenting.

START HERE

Projectile motion combines constant horizontal velocity with vertical acceleration due to gravity. Changing launch speed or angle changes the shape of the trajectory, but the horizontal and vertical motions can still be analyzed independently.

BUILD THE IDEA

What you should understand first

  • Resolve the launch velocity into horizontal and vertical components.
  • Connect launch angle to time of flight, maximum height and horizontal range.
  • See why gravity changes the trajectory even when horizontal motion is uniform.

TRY IT YOURSELF

Which launch angle gives the greatest range when launch and landing heights are equal?

  1. Keep speed and gravity fixed.
  2. Test several angles from 15° to 75°.
  3. Compare the measured ranges and then test complementary angle pairs such as 30° and 60°.
Read the visual:

With the ideal no-drag model, complementary angles produce the same range and 45° gives the maximum range.

WHY IT WORKS 01

Resolve the launch velocity into horizontal and vertical components.

Projectile motion combines constant horizontal velocity with vertical acceleration due to gravity. Changing launch speed or angle changes the shape of the trajectory, but the horizontal and vertical motions can still be analyzed independently. Focus on the relationship between the controlled variable and the measured response rather than treating the visual change as the explanation.

WHY IT WORKS 02

Connect launch angle to time of flight, maximum height and horizontal range.

With the ideal no-drag model, complementary angles produce the same range and 45° gives the maximum range. Use an extreme or boundary setting after the baseline trial to check whether the same reasoning still holds.

DO NOT MIX THESE UP

Common misconception

Range is not always maximized at 45° when launch and landing heights differ or when air resistance matters. Horizontal velocity is not accelerated by gravity in this ideal model.

PRACTICE CHALLENGE

Which launch angle gives the greatest range when launch and landing heights are equal?

  • Keep speed and gravity fixed.
  • Test several angles from 15° to 75°.
  • Compare the measured ranges and then test complementary angle pairs such as 30° and 60°.
Reveal the reasoning

With the ideal no-drag model, complementary angles produce the same range and 45° gives the maximum range. Range is not always maximized at 45° when launch and landing heights differ or when air resistance matters. Horizontal velocity is not accelerated by gravity in this ideal model.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Projectile is treated as a point mass.
  • Gravity is uniform and constant over the simulated region.
  • Air resistance, wind, lift and spin are ignored.

Model limitations

  • Real projectiles can lose speed to drag and deviate in wind.
  • The model is not intended for very long-range trajectories where Earth curvature or changing gravity matters.

CONNECT IT

Where this matters

  • Ballistics and sports trajectories
  • Water jets and fountains
  • Introductory orbital and kinematics modeling

WORDS THAT MATTER

Key vocabulary

Component
The part of a vector along a chosen axis.
Trajectory
The path followed by a moving object.
Range
Horizontal distance traveled before landing.