Projectile

Projectile Simulation Program

Interactive physics simulation with Visual Basic and VB.NET examples

How it works?

Projectile motion is a fundamental concept in physics that describes the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. This simulation demonstrates the parabolic path that projectiles follow, determined by the launching angle and initial speed.

The equations governing projectile motion are:

y = (v × sin(a)) × t - ½ × g × t²

x = (v × cos(a)) × t

Where v = launching speed, a = launching angle, g = gravity (9.8 m/s²), t = time

Below you'll find an interactive simulation, Visual Basic code examples for both VB6 and VB.NET, and practical exercises to deepen your understanding of physics programming.

Interactive Projectile Simulation

Adjust the parameters below to see how they affect the projectile's trajectory:

Initial Speed (m/s)

Launch Angle (°)

Gravity (m/s²)

Maximum Height: 0 m | Range: 0 m | Flight Time: 0 s

Visual Basic Implementation

Private Sub cmd_Draw_Click()
    Dim x As Single, y As Single
    Dim v As Single, t As Single, a As Single
    Dim g As Single
    
    ' Get input values
    v = Val(Txt_Speed.Text)
    a = Val(Txt_Angle.Text)
    g = 9.8 ' Acceleration due to gravity
    
    ' Clear previous drawing
    Pic_Curve.Cls
    t = 0
    
    ' Draw the ground
    Pic_Curve.Line (0, 120)-(Pic_Curve.Width, 120), vbGreen
    
    ' Calculate and plot trajectory
    Do
        t = t + 0.01
        y = v * Sin(a * 3.141592654 / 180) * t - 0.5 * g * (t ^ 2)
        x = v * Cos(a * 3.141592654 / 180) * t
        
        ' Plot point (adjusting for coordinate system)
        Pic_Curve.PSet (x, 120 - y), vbRed
        
        ' Exit loop when projectile hits ground
        If y < 0 Or x > Pic_Curve.Width Then
            Exit Do
        End If
    Loop
    
    ' Display results
    lblMaxHeight.Caption = "Max Height: " & Format(CalculateMaxHeight(v, a, g), "0.00") & " m"
    lblRange.Caption = "Range: " & Format(x, "0.00") & " m"
    lblFlightTime.Caption = "Flight Time: " & Format(t, "0.00") & " s"
End Sub

Private Function CalculateMaxHeight(v As Single, a As Single, g As Single) As Single
    ' Max height = (v² * sin²(a)) / (2 * g)
    CalculateMaxHeight = (v ^ 2) * (Sin(a * 3.141592654 / 180) ^ 2) / (2 * g)
End Function

Private Sub BtnSimulate_Click(sender As Object, e As EventArgs) Handles BtnSimulate.Click
    Dim v As Double = Double.Parse(TxtSpeed.Text)
    Dim a As Double = Double.Parse(TxtAngle.Text)
    Dim g As Double = 9.8
    Dim t As Double = 0
    Dim x, y As Double
    
    ' Clear previous drawing
    PicCanvas.Image = Nothing
    Using gfx As Graphics = Graphics.FromImage(PicCanvas.Image)
        ' Set up drawing surface
        gfx.SmoothingMode = SmoothingMode.AntiAlias
        gfx.Clear(Color.White)
        
        ' Draw ground
        gfx.DrawLine(Pens.Green, 0, PicCanvas.Height - 30, PicCanvas.Width, PicCanvas.Height - 30)
        
        ' Create pen for trajectory
        Using trajectoryPen As New Pen(Color.Blue, 2)
            Dim points As New List(Of PointF)
            
            ' Calculate trajectory points
            Do
                t += 0.01
                y = v * Math.Sin(a * Math.PI / 180) * t - 0.5 * g * Math.Pow(t, 2)
                x = v * Math.Cos(a * Math.PI / 180) * t
                
                ' Convert to canvas coordinates
                Dim canvasX As Single = x * 10
                Dim canvasY As Single = PicCanvas.Height - 30 - (y * 10)
                
                points.Add(New PointF(canvasX, canvasY))
                
                If y < 0 Or canvasX > PicCanvas.Width Then Exit Do
            Loop
            
            If points.Count > 1 Then
                gfx.DrawCurve(trajectoryPen, points.ToArray())
            End If
            
            gfx.FillEllipse(Brushes.Red, 0, PicCanvas.Height - 30, 8, 8)
        End Using
    End Using
    
    LblMaxHeight.Text = $"Max Height: {CalculateMaxHeight(v, a, g):F2} m"
    LblRange.Text = $"Range: {x:F2} m"
    LblFlightTime.Text = $"Flight Time: {t:F2} s"
    
    PicCanvas.Invalidate()
End Sub

Private Function CalculateMaxHeight(v As Double, a As Double, g As Double) As Double
    Return (Math.Pow(v, 2) * Math.Pow(Math.Sin(a * Math.PI / 180), 2)) / (2 * g)
End Function

Understanding the Projectile Simulation

The projectile simulation uses fundamental physics equations to calculate the path of an object launched at an angle:

Key Equations

x = v × cos(θ) × t

y = v × sin(θ) × t - ½ × g × t²

Where:

x = Horizontal position (meters)
y = Vertical position (meters)
v = Initial velocity (m/s)
θ = Launch angle (degrees)
t = Time (seconds)
g = Acceleration due to gravity (9.8 m/s²)

Understanding the Projectile Simulation

The projectile simulation uses fundamental physics equations to calculate the path of an object launched at an angle:

Key Equations

x = v × cos(θ) × t

y = v × sin(θ) × t - ½ × g × t²

Where:

x = Horizontal position (meters)
y = Vertical position (meters)
v = Initial velocity (m/s)
θ = Launch angle (degrees)
t = Time (seconds)
g = Acceleration due to gravity (9.8 m/s²)

Practice Exercises

Test your understanding with these programming exercises:

Exercise 1: Air Resistance

Modify the simulation to account for air resistance. Add a drag coefficient input and adjust the equations to include drag force:

Drag force = ½ × ρ × v² × Cd × A
Where ρ = air density (1.2 kg/m³), Cd = drag coefficient, A = cross-sectional area
Implement Euler integration to update velocity and position

Exercise 2: Multiple Projectiles

Enhance the program to simulate multiple projectiles simultaneously:

Allow users to add multiple projectiles with different speeds and angles
Display each trajectory in a different color
Add collision detection between projectiles
Implement a "compare" mode to show differences in trajectories

Exercise 3: Target Practice Game

Create a game where players try to hit targets with projectiles:

Place targets at random positions on the screen
Let players adjust angle and power (speed)
Add wind effects that vary with each shot
Keep score based on target distance and number of attempts