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Mechanics learning guide

Projectile Motion Simulator and Complete Guide

Explore projectile motion interactively, derive the core equations, test launch angles, and solve a worked range example with a free browser lab.

Open the projectile motion lab →

Launch, pause, measure, and compare trajectories without installing software.

Start with the model

Concept overview

Projectile motion describes an object moving under gravity after launch. In the simplest model, horizontal and vertical motions can be analysed independently: horizontal velocity stays constant while vertical velocity changes by the gravitational acceleration. The curved path is not caused by a fading horizontal force. It emerges because steady horizontal motion and accelerating vertical motion happen at the same time.

The interactive lab lets you change launch speed, angle, height, gravity, and drag, then compare the predicted path with the plotted motion. Start with air resistance off so the ideal equations match the experiment. Add drag only after you can explain the ideal case, because drag couples the two directions and removes the simple symmetry between ascent and descent.

Concept 1

Independent components

Resolve the initial velocity into horizontal and vertical components. Gravity changes only the vertical component in the ideal model, so each direction can be calculated on its own and recombined.

Concept 2

Time controls the path

Both position equations use the same elapsed time. Finding flight time from the vertical motion and substituting it into the horizontal motion gives the range.

Concept 3

Model boundaries

The familiar 45-degree maximum-range result assumes equal launch and landing heights, constant gravity, and no air resistance. Change any of those assumptions and the best angle can change.

Guided investigation

Which angle gives the greatest ideal range?

  1. 1Set launch and landing heights equal, choose Earth gravity, and turn air resistance off.
  2. 2Hold launch speed constant and record the range at 15, 30, 45, 60, and 75 degrees.
  3. 3Compare complementary angle pairs such as 30 and 60 degrees, then explain the matching ranges.
  4. 4Turn drag on, repeat the sweep, and identify how the range-maximising angle changes.

Evidence to record

Create a table with angle, horizontal speed, vertical speed, flight time, maximum height, and range. State which assumptions explain your ideal results and which assumption drag breaks.

Equations and variables

x = x0 + (v0 cos theta)t

Horizontal position for constant horizontal velocity.

  • • x and x0: final and initial horizontal position
  • • v0: launch speed
  • • theta: launch angle
  • • t: elapsed time

y = y0 + (v0 sin theta)t - (1/2)gt^2

Vertical position under constant downward gravitational acceleration.

  • • y and y0: final and initial height
  • • g: gravitational acceleration
  • • v0 sin theta: initial vertical speed
  • • t: elapsed time

Worked example

Apply the model

A ball is launched from level ground at 20 m/s and 30 degrees. Ignore drag and use g = 9.8 m/s^2. Find its ideal range.

  1. Step 1: Use the level-ground range relation R = v0^2 sin(2 theta) / g.
  2. Step 2: Substitute: R = 20^2 x sin(60 degrees) / 9.8 = 400 x 0.866 / 9.8.

Answer: The ideal range is about 35.3 m. The value is a model prediction; measured range will differ when drag, wind, spin, or unequal heights matter.

Misconceptions to test

Common claim

“A horizontal force keeps a projectile moving forward.”

Correction: After launch, the ideal model has no horizontal force. Horizontal velocity persists because no horizontal net force changes it.

Common claim

“Heavier objects fall faster in the ideal model.”

Correction: With air resistance neglected, all projectiles have the same gravitational acceleration regardless of mass.

Teacher-ready worksheet

Projectile motion investigation sheet

  1. 1.Write a testable prediction before changing the launch angle.
  2. 2.Record five controlled trials in a labelled data table.
  3. 3.Sketch velocity vectors at launch, apex, and landing.
  4. 4.Explain one difference between the ideal and drag-enabled runs.
  5. 5.Use one equation to check a measured result.

Print or save this page as PDF to use the investigation and worksheet offline.

Knowledge check

Check your understanding

Answer four questions about components, range, and model assumptions, with immediate verified feedback.

Take the projectile motion knowledge check →

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