# Example 3-2
D1 = [0, 22] km; km
D2 = PolarVec(47 km, -60 deg); km
D3 = D1 + D2; km
mag(D3); km
PolarAngle(D3); deg
atan2(D3[2], D3[1]); deg
atan2(component(D3,2), component(D3,1)); deg

# Example 3-3
D1 = PolarVec(620 km, 0 deg)
D2 = PolarVec(440 km, -45 deg)
D3 = PolarVec(550 km, (180 + 53) deg)
DR = D1 + D2 + D3
mag(DR); km
PolarAngle(DR); deg

# Example 3-4
D1 = [ 0, 22] km
D2 = [ 23.5, -40.7] km
D3 = D1 + D2
mag(D3); km
PolarAngle(D3); deg
atan2(component(D3,2), component(D3,1)); deg

# Example 3-5
BEGIN
t = 1 s
r = [ (5 m/s) * t + (6 m / s^2) * t^2, 7 m - (3 m/s^3)*t^3]
v = [ (5 m/s) + 2 * (6 m / s^2) * t,  -3 *  (3 m/s^3)*t^2]
a = [ 2 * (6 m / s^2),   -6 *  (3 m/s^3)*t]
END
func(t,2 s)
func(t,3 s)

# Example 3-6
y = -50 m
tt = sqrt(2 * y / (-grav()))
x = 90 m
vx0 = x / tt

# Example 3-7
vy0 = 12.0 m/s
tt = vy0 / grav()
y = vy0 * tt - 0.5 * grav() * tt^2
t2 = 2 * vy0 / grav()
vx0 = 16 m/ s
x = vx0 * t2

# Example 3-10
R = 320 m
v0 = 60 m / s
q1 = (1/2) * asin(R * grav() / v0^2); deg
q2 = 90 deg - q1; deg

# Example 3-11
y = -1 m
y0 = 0
vy0 = 12 m/s
BEGIN
   tt = 1 s
   eq = y0 + vy0 * tt - 0.5 * grav() * tt^2 - y
   x = vy0 * tt
END
tt = 2 s
solve(eq,tt)
tt = 0 s
solve(eq,tt)

# Example 3-12
y = -200 m
tt = sqrt(-2 * y / grav())
vx0 = 70 m/s
x = vx0 * tt
x = 400 m
t2 = x / vx0
vy0 = (y + 0.5 * grav() * t2^2) / t2
vy = vy0 - grav() * t2

# Example 3-14
vws = 1.2 m/s
vbw = 1.85 m/s
q = asin(vws / vbw); deg

# Example 3-15
vws = 1.2 m/s
vbw = 1.85 m/s
vbs = sqrt(vbw^2 + vws^2)
q = atan(vws / vbw); deg
tt = 59.5 s
d = vws * tt

# Example 3-16
MKS(kph, deg)
v1 = [0, 40 kph]
v2 = [40 kph, 0]
v12 = v1 - v2
mag(v12)
PolarAngle(v12)

# Homework Problems:

TBD