Home/Physics I Year/Team 2
Team 2

Projectile Motion Simulator

Build an app that calculates the range, maximum height, and time of flight for a projectile launched at a given angle and velocity. Includes a visual trajectory on Canvas.

🎯 Learning Goals

  • ▹ Understand independence of Horizontal and Vertical motion
  • ▹ Master kinematic equations for parabolic paths
  • ▹ Learn the impact of launch angle on Range and Height
  • ▹ Implement Canvas plotting using math simulation loops

🌎 Why This Matters

From sports (bowling a cricket ball or shooting a basketball) to satellites and robotics, predicting where an object will land is vital. This simulator shows you the invisible math that controls everything moving through the air.

📖Understanding Projectile Motion

Theory Masterclass
"

Projectile motion is when an object is launched into the air and follows a curved (parabolic) path under the influence of gravity only. Think of throwing a cricket ball — it goes up, forward, and then comes back down forming a curve. Key Decomposition: The motion is split into TWO independent parts: 1. Horizontal (x-direction): Constant velocity (no acceleration), vₓ = v₀ × cos(θ) 2. Vertical (y-direction): Accelerated by gravity, v_y = v₀ × sin(θ) - g×t Key Variables: v₀ = Initial velocity (how fast you throw) θ = Launch angle (the direction) g = Gravitational acceleration = 9.8 m/s² t = Time Time of Flight: The total time the projectile is in the air. T = 2 × v₀ × sin(θ) / g Maximum Height: The highest point reached. H = v₀² × sin²(θ) / (2g) Range: The horizontal distance traveled. R = v₀² × sin(2θ) / g At θ = 45°, the range is MAXIMUM for a given velocity.

Mathematical Foundation

fxTime of Flight: T = 2v₀sin(θ) / g
fxMax Height: H = v₀²sin²(θ) / 2g
fxRange: R = v₀²sin(2θ) / g
fxHorizontal velocity: vₓ = v₀cos(θ)
fxVertical velocity: v_y = v₀sin(θ) - gt

🎨Part A — Designer View (UI Design)

Open MIT App Inventor → Switch to Designer view. Follow each step below to build the interface.

1

Set up the screen

Title: "Projectile Motion Simulator" Set ScreenOrientation to Portrait.

2

Create input section

Add Labels and TextBoxes: - "Initial Velocity (m/s)": TextBox VelocityInput (NumbersOnly) - "Launch Angle (degrees)": TextBox AngleInput (NumbersOnly) - Optional: Slider for angle (MinValue=0, MaxValue=90) for interactive feel

3

Add Launch button

Add a big Button: "LAUNCH 🚀" Set it to green, bold, full width. This triggers all calculations.

4

Create results display

Add a Card-like section with Labels: - RangeLabel: "Range: — m" - HeightLabel: "Max Height: — m" - TimeLabel: "Time of Flight: — s" - VxLabel: "Horizontal Velocity: — m/s" - VyLabel: "Initial Vertical Velocity: — m/s"

5

Add Canvas for trajectory

Add a Canvas component: Width: Fill Parent Height: 250 pixels BackgroundColor: Dark This will show the parabolic path!

6

Add angle comparison section

Add a Button: "Compare 30° vs 45° vs 60°" Three Labels to show range at each angle for comparison. This demonstrates that 45° gives maximum range.

🧩Part B — Blocks View (Logic & Calculation)

Switch to Blocks view. Now add the logic that makes your app actually work.

1

Convert angle to radians

MIT App Inventor trigonometry uses DEGREES by default. But just to be safe, create a procedure: toRadians(degrees) = degrees × π / 180 Actually, App Inventor's sin/cos blocks accept degrees directly! So you can use sin(angle) directly where angle is in degrees.

2

Calculate Time of Flight

When LaunchButton.Click: 1. Read v0 = number(VelocityInput.Text) 2. Read angle = number(AngleInput.Text) 3. T = (2 × v0 × sin(angle)) / 9.8 4. Set TimeLabel.Text = "Time of Flight: " + round(T×100)/100 + " s"

3

Calculate Maximum Height

H = (v0 × v0 × sin(angle) × sin(angle)) / (2 × 9.8) Set HeightLabel.Text = "Max Height: " + round(H×100)/100 + " m" Note: sin(angle) × sin(angle) = sin²(angle)

4

Calculate Range

R = (v0 × v0 × sin(2 × angle)) / 9.8 Set RangeLabel.Text = "Range: " + round(R×100)/100 + " m" Note: sin(2×angle) uses the double angle.

5

Calculate component velocities

vx = v0 × cos(angle) vy = v0 × sin(angle) Set VxLabel.Text = "Horizontal Velocity: " + round(vx×100)/100 + " m/s" Set VyLabel.Text = "Initial Vertical Velocity: " + round(vy×100)/100 + " m/s"

6

Draw trajectory on Canvas

After calculating, draw the path: 1. Canvas1.Clear 2. Set Canvas paint color to green 3. Loop t from 0 to T in small steps (0.05): x = vx × t y = vy × t - 0.5 × 9.8 × t² Scale x and y to fit Canvas: canvasX = (x / R) × Canvas1.Width canvasY = Canvas1.Height - (y / H) × Canvas1.Height × 0.8 Canvas1.DrawCircle(canvasX, canvasY, 2) This plots dots along the parabolic path!

7

Build the comparison feature

When CompareButton.Click: Calculate range for 30°, 45°, and 60° with the same v0: R30 = v0² × sin(60°) / 9.8 R45 = v0² × sin(90°) / 9.8 R60 = v0² × sin(120°) / 9.8 Display all three. Students will see that R45 > R30 = R60!

8

Input validation

Check: velocity must be > 0, angle must be between 0 and 90. Show Notifier alert if values are out of range.

🧪Testing Your App

  • ✓v₀=20 m/s, θ=45° → R≈40.8m, H≈10.2m, T≈2.88s
  • ✓v₀=10 m/s, θ=30° → R≈8.83m, H≈1.28m, T≈1.02s
  • ✓At 90°: Range=0 (goes straight up and comes back)
  • ✓At 0°: Range=0 (doesn't go up at all)
  • ✓Range at 30° should equal range at 60° (complementary angles)

🚀Bonus Challenges

Extra credit — impress your instructor

  • ★Add air resistance effect (simple drag model)
  • ★Let users tap the Canvas to set the launch angle visually
  • ★Add a 'hit the target' game mode with a target at random distance
  • ★Show velocity components as arrows on the Canvas at different time points
← Back to Physics I YearReview Basics →