If you set the compile-time variable DEBUGGING to True, then the program draws the position where the cannon ball should ideally cross the Y coordinate where it was launched. If the ball started at ground level and the ground were flat, this is where the ball would land. It calculates this position using the formula:

    Distance = 2 * V^2 * Sin(T) * Cos(T) / g

Here g is the acceleration due to gravity, which is 9.8 meters per second. The program redraws TICKS_PER_SECOND times per second so the acceleration per tick is 9.8/(TicksPerSecond^2).

Private Sub cmdFire_Click(ByVal sender As System.Object, _
    ByVal e As System.EventArgs) Handles cmdFire.Click
    Dim gr As Graphics = picCanvas.CreateGraphics()

    ' Redraw.
    DrawField(gr)

    ' Get the speed.
    Dim speed As Single
    Try
        speed = CSng(txtSpeed.Text)
    Catch ex As Exception
        MessageBox.Show("Invalid speed", "Invalid Speed", _
            MessageBoxButtons.OK, _
            MessageBoxIcon.Exclamation)
        Exit Sub
    End Try
    If speed < 1 Then
        MessageBox.Show("Speed must be at least 1 mps", _
            "Invalid Speed", MessageBoxButtons.OK, _
            MessageBoxIcon.Exclamation)
        Exit Sub
    End If

    ' Get the speed components in meters per tick.
    m_Vx = speed * System.Math.Cos(m_Theta) / _
        TICKS_PER_SECOND
    m_Vy = -speed * System.Math.Sin(m_Theta) / _
        TICKS_PER_SECOND ' Negative to go up.

    ' Disable UI elements.
    cmdFire.Enabled = False
    txtDegrees.Enabled = False
    txtSpeed.Enabled = False
    Cursor = Cursors.WaitCursor
    Application.DoEvents()

#Const DEBUGGING = True
#If DEBUGGING Then
    ' Draw the location where the cannon ball
    ' should pass the Y position where it started.
    ' Distance = 2 * V^2 * Sin(T) * Cos(T) / g = V^2 *
    ' Sin(2*T) / g
    gr.DrawEllipse(Pens.Blue, _
        CSng(m_BulletX + 2 * speed ^ 2 * Sin(m_Theta) * _
            Cos(m_Theta) / 9.8), _
        CSng(m_BulletY), CANNON_HGT, CANNON_HGT)
#End If

    ' Start moving the cannon ball.
    tmrMoveShot.Enabled = True
End Sub

' Acceleration in meters per tick squared.
Private Const m_YAcceleration As Single = 9.8 / _
    TICKS_PER_SECOND ^ 2

Private m_BulletX As Double
Private m_BulletY As Double
Private m_Vx As Double
Private m_Vy As Double

Private Sub tmrMoveShot_Tick(ByVal sender As System.Object, _
    ByVal e As System.EventArgs) Handles tmrMoveShot.Tick
    ' Erase the cannon ball's previous position.
    Dim gr As Graphics = picCanvas.CreateGraphics()
    Dim br As New SolidBrush(picCanvas.BackColor)
    gr.FillEllipse(br, _
        CSng(m_BulletX), CSng(m_BulletY), _
        CANNON_HGT, CANNON_HGT)
    br.Dispose()

    ' Move the cannon ball.
    m_Vy = m_Vy + m_YAcceleration
    m_BulletX = m_BulletX + m_Vx
    m_BulletY = m_BulletY + m_Vy

    ' Draw the new cannon ball.
    gr.FillEllipse(Brushes.Black, _
        CSng(m_BulletX), CSng(m_BulletY), _
        CANNON_HGT, CANNON_HGT)

    ' See if we should stop.
    If (m_BulletY > picCanvas.ClientRectangle.Height) Or _
        (m_BulletX > picCanvas.ClientRectangle.Width) Then _
        ' Stop running.
        tmrMoveShot.Enabled = False

        ' Re-enable UI elements.
        cmdFire.Enabled = True
        txtDegrees.Enabled = True
        txtSpeed.Enabled = True
        Me.Cursor = Cursors.Default
    End If
End Sub