Projectile Motion Lesson Plan with a Simulation

This projectile motion lesson plan uses a free interactive simulation to let students discover, in one class period, why 45° gives the longest range, why 30° and 60° land in the same place, and why doubling the speed quadruples the distance. Everything is ready to use: learning goals, setup, prediction questions, a step-by-step activity with a data table and the values students should get, discussion questions with answers, an air resistance extension and ideas for differentiation. The numbers below come from the simulation's own model, so you can check student work at a glance.

Lesson at a glance

• Level: grades 9–12 (ages 14–18), introductory physics or physics.
• Time: one 50–60 minute period, plus an optional 20-minute extension.
• Prior knowledge: velocity as a vector, sine and cosine for components, motion with constant acceleration.
• Format: pairs on laptops or tablets, or the whole class with one projector.
• Simulation: Projectile motion – trajectory and air resistance.

Learning goals

By the end of the lesson, students can:

1. Describe projectile motion as two independent motions: constant velocity horizontally, constant acceleration g vertically.
2. Measure range, maximum height and time of flight, and relate them to launch angle and launch speed.
3. Explain why complementary angles give the same range and why 45° gives the maximum range on level ground without air resistance.
4. Use R = v²·sin2θ/g to predict a range, then check it.
5. (Extension) Describe how air resistance shortens the path and lowers the best launch angle.

What the simulation does

It helps to know the model before you teach with it. The simulation has four screens:

• Intro: set launch height (0–15 m), launch angle (0–90°), initial speed (5–30 m/s) and projectile, then press Fire. A target sits on the ground at 12 m by default; drag it or use the slider (1–80 m). The shot counts as a hit when it lands within about 0.75 m of the target.
• Vectors: the same launch, with arrows for vx, vy, the resultant v and the acceleration.
• Air Resistance: an Air resistance checkbox and an altitude slider (0–9,000 m) for a basketball, steel ball or shuttlecock.
• Lab: set mass, diameter, drag coefficient and gravity (Earth 9.8, Moon 1.62, Mars 3.71 or a custom value).

On the Intro and Vectors screens there is no air resistance and g = 9.8 m/s². That matches the textbook model, so the formulas below apply exactly. The readout shows range, max height and time of flight to two decimal places. Tap the path to probe a point (time, x, y), or drag on the canvas to measure with the tape measure. The last four trails stay on screen for comparison until you press Clear Trails.

Materials and setup before class

Materials: one device per pair (or a projector), the data table below on paper or in a shared document, and a calculator.

Setup (10 minutes, once):

1. Open the simulation and set the Intro screen to launch height 0 m, angle 45°, speed 15 m/s. These are also the defaults.
2. Click Share and create a link for each class, for example "Physics · Period 2". The link pins the current settings, so every student starts identically.
3. Optional: in the Questions tab, add the three prediction questions below as "Before, as a prediction", with Ask again after the simulation ticked. Students then have to commit before the simulation unlocks. The Predict–Observe–Explain guide explains why this works.
4. Post the link, or show the QR code in present mode so students can scan it from the board.

Lesson sequence

1. Hook and predictions (8 minutes)

Show a 45° shot on the projector without telling students the numbers. Then ask them to commit, on paper or on the link:

• P1. "At 15 m/s, which launch angle sends the ball farthest: 15°, 30°, 45°, 60° or 75°?"
• P2. "Ball A is launched at 30°, ball B at 60°, at the same speed. Which lands farther: A, B, or the same?"
• P3. "If you double the launch speed, the range will… stay the same, double, triple or quadruple?"

Expect many students to pick 60° for P1 ("higher means farther") and A or B for P2. Don't correct anyone yet.

2. Angle and range: data collection (15 minutes)

Pairs stay on the Intro screen with height 0 m and speed 15 m/s. They fire at each angle in the table, record the readout and sketch each trail. The last two columns are for you; leave them blank on the student copy.

Angle	Range R (m)	Max height H (m)	Time of flight T (s)	Expected R	Expected H
15°				11.48	0.77
30°				19.88	2.87
45°				22.96	5.74
60°				19.88	8.61
75°				11.48	10.71

Expected times of flight: 0.79 s, 1.53 s, 2.16 s, 2.65 s and 2.96 s.

These come from R = v²·sin2θ/g, H = v²·sin²θ/(2g) and T = 2v·sinθ/g with v = 15 m/s and g = 9.8 m/s². For 45°: R = 225 × 1 / 9.8 = 22.96 m. Because the Intro screen has no air resistance, students' readings should match to the last digit. If a pair's numbers are off, they almost always changed the launch height or the speed by accident.

Then ask pairs to write two patterns they see. Good answers: "R is the same for 15° and 75°, and for 30° and 60°" and "H and T keep increasing with angle, but R peaks at 45°."

3. Speed and range (7 minutes)

Keep 45° and fire at 10, 15, 20 and 30 m/s. Expected ranges: 10.20 m, 22.96 m, 40.82 m and 91.84 m.

Ask: "From 10 to 20 m/s, how many times farther?" Answer: 40.82 ÷ 10.20 = 4.0. Doubling the speed quadruples the range. Have students check P3.

4. Vectors: why the path is a parabola (8 minutes)

Switch to the Vectors screen at 15 m/s and 45°. Turn on vx, vy and acceleration, fire, and tap different points along the path.

Students should notice:

• The vx arrow never changes length: vx = 15 × cos45° = 10.61 m/s everywhere.
• The vy arrow shrinks to zero at the top, then grows downward.
• The acceleration arrow is the same everywhere: g, straight down.

Ask: "What is the speed at the very top?" Many students say zero. The probe shows vy = 0 but v = vx = 10.61 m/s. Constant horizontal velocity plus constant vertical acceleration is exactly what gives a parabola.

5. Target challenge (7 minutes)

Back on Intro, at 15 m/s with the target at 12 m: "Find two different angles that hit the target."

Solving 12 = 225·sin2θ/9.8 gives sin2θ = 0.523, so θ ≈ 15.8° or 74.2°. With whole-number angles, 15°, 16°, 74° and 75° all count as hits; 16° and 74° land closest, at 12.17 m. Pairs who find one angle and then use symmetry (90° − θ) to find the other have understood the main idea of the lesson.

6. Discussion (8 minutes)

Use these questions with the whole class. Short answers follow each one.

1. Why do 30° and 60° land in the same place? The 60° ball stays in the air longer (2.65 s versus 1.53 s) but moves forward more slowly (vx = 7.50 m/s versus 12.99 m/s). The products are equal: 19.88 m. Mathematically, sin60° = sin120°, so sin2θ is the same for complementary angles.
2. Why is 45° the best angle? sin2θ has its maximum value, 1, when 2θ = 90°. Below 45° the ball lands too soon; above 45° it moves forward too slowly.
3. How do the maximum heights at 30° and 60° compare? 2.87 m versus 8.61 m, a ratio of 1 to 3, because sin²30° = 0.25 and sin²60° = 0.75.
4. Does a steel ball go farther than a basketball on the Intro screen? No. Without air resistance, mass does not appear in any of the equations, and both follow the same path.
5. Why does doubling the speed quadruple the range? Both the time in the air and the horizontal speed double, so their product goes up four times.

Then return to the predictions. If you used the link, open the results and show the Prediction and After columns side by side. Students like seeing how many minds changed.

7. Exit check (5 minutes)

Two quick questions, on paper or as number questions on the link:

• "At 20 m/s and 45°, what is the range?" Answer: 40.82 m (accept ± 0.5).
• "At 15 m/s, which other angle gives the same range as 25°?" Answer: 65° (both give 17.59 m).

The formative assessment guide shows how to set these up so they are checked automatically and compared across classes.

Extension: air resistance, launch height and other planets

For strong groups or a second lesson, use the screens beyond Intro.

Air resistance. On the Air Resistance screen, choose the basketball, 15 m/s, 45°, sea level, tick Air resistance and fire. The range drops from 22.96 m to about 16.7 m, and the readout shows the no-drag values underneath for comparison. The path is no longer symmetric: it comes down more steeply than it went up.

Then compare projectiles at 45°:

Projectile	Range with drag	Best angle with drag
Steel ball	about 22.0 m	about 45°
Basketball	about 16.7 m	about 43° (40°–45° are within 0.1 m)
Shuttlecock	about 4.0 m	about 34° (4.1 m)

The lesson here: air resistance matters most for light objects with a large area, and it pushes the best angle below 45°. Raise the altitude to 9,000 m and the basketball's range grows to about 20.3 m, because the air is thinner.

Launch height. On Intro, set the height to 10 m, 15 m/s, 45°: the range becomes 30.49 m. Now 45° is no longer the best angle. Around 36° gives about 31.4 m. Ask students to explain why a launch from above the landing level favors a flatter shot.

Other planets. On the Lab screen with air resistance off, choose the Moon (g = 1.62 m/s²). At 15 m/s and 45°, the range is 225 ÷ 1.62 = 138.89 m. On Mars (g = 3.71 m/s²) it is 60.65 m. Ask: "How does range depend on g?" Answer: R is inversely proportional to g.

Differentiation

Support:

• Pin the starting values on the link and give students a table with the angle column already filled.
• Use three angles (30°, 45°, 60°) instead of five.
• Give sentence starters for the patterns: "When the angle increases from 45° to 60°, the range…"
• Pair students so that one operates the simulation and one records, then swap halfway.

Stretch:

• Derive R = v²·sin2θ/g from the component equations before checking it in the simulation.
• Find the best angle from a 10 m platform by trial and error, then explain the result.
• Predict the basketball's range with drag before firing, and explain why no simple formula gives it.
• Use the Lab screen to find which custom g sends a 15 m/s, 45° shot exactly 50 m (g = 225 ÷ 50 = 4.5 m/s²), then test it.

English learners: the simulation is available in six languages. Create a second link in the student's language so the labels are familiar while the class discussion stays in English.

Standards alignment

This lesson aligns with typical high-school kinematics units on two-dimensional and projectile motion, including the kinematics unit of AP Physics 1. NGSS has no performance expectation dedicated to projectile motion, so we don't claim one. The lesson does exercise three NGSS science and engineering practices: Planning and Carrying Out Investigations, Analyzing and Interpreting Data, and Using Mathematics and Computational Thinking.

For a full inquiry structure around this activity, see the 5E lesson plan guide, and for running it as a lab write-up, how to create a virtual lab activity.

FAQ

Does the simulation include air resistance?

Only on the Air Resistance and Lab screens, and only when you tick Air resistance. The Intro and Vectors screens use the ideal model with no drag and g = 9.8 m/s².

Why do my students' numbers differ slightly from a textbook that uses g = 10?

The simulation uses g = 9.8 m/s². With g = 10, the 45° range at 15 m/s would be 22.50 m instead of 22.96 m. Tell students which value to use before they calculate.

Can students do this lesson on phones?

Yes. Students open the link without an account, and the controls work on touch screens. A tablet or laptop makes reading the readout and recording the table easier.

How long does the extension take?

About 20 minutes for the air resistance comparison alone. Launch height and other planets add 10 minutes each.