n = 15108099
k = n Mod 10000
T = n Mod 100
m = n Mod 35
a = n Mod 25
L = n Mod 10
nn = 2 * m + 2
pi = 4 * Atn(1)
g = 10
x = 11 - 1 / T - 0.1
y = 2.5 - 1 / k - 0.1


t1 = (2 * y - x + Sqr((x - 2 * y) ^ 2 + 4 * x * (x + y))) / (2 * x)
'
v_min = Sqr(g * x ^ 2 * (1 + t1 ^ 2) / (2 * (x * t1 - y)))
' angle for minimum velocity:
MsgBox "angle for minimum velocity:"
MsgBox Atn(t1) * 180 / (4 * Atn(1))
MsgBox "degrees"
MsgBox "minimum velocity:"
MsgBox v_min
MsgBox "meters per second"


MsgBox "If the initial velocity of release is"
v = 30
MsgBox v
MsgBox "meters per second"
MsgBox "then"

MsgBox "there are two possible angles of release for the shuttle to fly just above the net"

a = g * x ^ 2 / 2 / v ^ 2
b = -x
c = g * x ^ 2 / 2 / v ^ 2 + y
c = a + y
N1 = (-b - Sqr(b ^ 2 - 4 * a * c)) / (2 * a)
'N1 = Atn(N1)
aN1 = Atn(N1)
DaN1 = 180 * aN1 / pi
MsgBox DaN1
MsgBox "degrees"

MsgBox "and"

N2 = (-b + Sqr(b ^ 2 - 4 * a * c)) / (2 * a)
'N2 = Atn(N2)

' aN is an angle in radians.
aN2 = Atn(N2)

' DaN is angle in degrees.
DaN2 = 180 * aN2 / pi
MsgBox DaN2
MsgBox "degrees"

'

MsgBox "there is the distance at which the ball hits the top corner"

a = g * (1 + N1 ^ 2) / 2 / v ^ 2
b = -N1
c = y
X1 = (-b + Sqr(b ^ 2 - 4 * a * c)) / (2 * a)
' minus before the square root has no physical meaning here
MsgBox x

MsgBox "meters"

'MsgBox "and"

a = g * (1 + N2 ^ 2) / 2 / v ^ 2
b = -N2
c = y
X2 = (-b + Sqr(b ^ 2 - 4 * a * c)) / (2 * a)
' minus before the square root has no physical meaning here
'MsgBox X2

'MsgBox "meters"

MsgBox "there are 2 times: 1 for each path"

'N1 = Atn(N1)

t1 = x / (v * Cos(aN1))
MsgBox t1

MsgBox "seconds"

MsgBox "and"

'N2 = Atn(N2)
t2 = x / (v * Cos(aN2))
MsgBox t2

MsgBox "seconds"


MsgBox "there are 2 curves lengths: 1 for each path"


' Integrating using Simpson rule to calculate the curves lengths:

a = 0

Dim f(99)

b = x
'b = X2
'nn = 98
h = (b - a) / nn
'
For kk = 0 To nn
x = a + kk * (b - a) / nn
f(kk) = Sqr(1 + (N1 - g * x * (1 + N1 ^ 2) / v ^ 2) ^ 2)
'f(kk) = Sqr(1 + (N2 - g * x * (1 + N2 ^ 2) / v ^ 2) ^ 2)
Next kk
'
i2j = 0
For j = 1 To nn / 2 - 1
i2j = i2j + f(2 * j)
Next j
'
i2jm1 = 0
For j = 1 To nn / 2
i2jm1 = i2jm1 + f(2 * j - 1)
Next j
'
L1 = (f(0) + 2 * i2j + 4 * i2jm1 + f(nn)) * h / 3
'
MsgBox L1

MsgBox "meters"

MsgBox "and"


'b = X1
b = x
'n = 88
h = (b - a) / nn
'
For kk = 0 To nn
x = a + kk * (b - a) / nn
'f(kk) = Sqr(1 + (N1 - g * x * (1 + N1 ^ 2) / v ^ 2) ^ 2)
f(kk) = Sqr(1 + (N2 - g * x * (1 + N2 ^ 2) / v ^ 2) ^ 2)
Next kk
'
i2j = 0
For j = 1 To nn / 2 - 1
i2j = i2j + f(2 * j)
Next j
'
i2jm1 = 0
For j = 1 To nn / 2
i2jm1 = i2jm1 + f(2 * j - 1)
Next j
'
L2 = (f(0) + 2 * i2j + 4 * i2jm1 + f(nn)) * h / 3
'
MsgBox L2

MsgBox "meters"

MsgBox "there are 2 average velocities: 1 for each path"

aV1 = L1 / t1
MsgBox aV1

MsgBox "meters per second"

MsgBox "and"


aV2 = L2 / t2
MsgBox aV2

MsgBox "meters per second"