# Example 13.1
t = 1 s
a = grav()
v = a * t
h = (a/2) * t^2
v0 = 6 m/s
t = v0 / a
h = (a/2) * t^2



# Example 13.2
FPS
v0 = 75 mph
t0 = 4 s
a0 = v0 / t0
h = 0.5 * a0 * (4 s)^2 + v0 * 6 s



# Example 13.3
t1 = 2 s
t2 = 4 s
a1 = 2 m/s^2
v0 = 180 km/hr
v = v0 + a1 * (t2 - t1)
h = v0 * (t2 - t1) + 0.5 * a1 * (t2^2 - t1^2)


# Example 13.4
BEGIN
   t = 1 
   v = 10
   e = t - 250 * (1 / v - 1 / 80)
END
solve(e, t)
h = 250 * log(80 / v)


# Example 13.7
q = 20 deg
BEGIN
  t = 1
  x = 9.4 * t
  y = -3.42 * t - 4.905 * t^2
  vx = 9.4
  vy = -3.42 - 2 * 4.905 * t
  e = y - (-x - 3)
END
solve(e, t)
q = 45 deg
e = [cos(q) , sin(q)]
v = [vx,vy]
v1 = dot(e, v) * e
sqrt(dot(v,v) - dot(v1,v1))


# Example 13.8
om1 = 10000 rpm
om2 = 1000 rpm
a = 0.02 / s
t = (1 / a) * log(om1 / om2)
q = (1 / a) * (om1 - om2); rev



# Example 13.9
r = 400
t = 10
h = t^2 + (0.1 / 3) * t^3
at = 2 + 0.2 * t
v = 2 * t + 0.1 * t^2
an = v^2 / r
mag([at,an])



# Example 13.11
t = 4
ax = 0.6 * t
ay = 1.8 -0.36 * t
vx = 0.3 * t^2
vy = 1.8 * t - 0.18 * t^2
v = [vx,vy]
e = v / mag(v)
a = [ax, ay]
at = dot(e, a)
mag(a)
an = sqrt(dot(a,a) - at^2)
rho = dot(v,v) / an



# Example 13.12
BEGIN
  a = 626 
  b = a * (626)^2
  e2 = sqrt(a * b) - log(19) / 240
END
solve(e2,a)


# Example 13.14
t = 0.8
r = 1 - 0.5 * cos(2 * pi() * t)
q = 0.5 - 0.2 * sin(2 * pi() * t)

drdt = 2 * pi() * 0.5 * sin(2 * pi() * t)
dqdt = -0.2 * 2 * pi() * cos(2 * pi() * t)
vr = drdt
vq = r * dqdt

vx = vr * cos(q) - vq * sin(q)
vy = vr * sin(q) + vq * cos(q)
v = [vx, vy] 
mag(v)

# Example 13.15
om = 4 rad/s
q = 45 deg
r = 0.15 m / (1 + 0.5 * cos(q))
drdt = 0.075 m * sin(q) / (1 + 0.5 * cos(q))^2 * om
vr = drdt
vq = r * om
vx = vr * cos(q) - vq * sin(q)
vy = vr * sin(q) + vq * cos(q)
v = [vx, vy] 
mag(v)



# Example 13.16
BEGIN
   vb = [2, 0] m/s
   x = 1 m/s
   va = PolarVec(x, 135 deg)
   vab = va - vb
   err = mag(vab) - 5 m/s
END
solve(err, x)



# Example 13.17
BEGIN
  c = 1 / s
  t = 2 s
  h = 0.9 * grav() / c^2 * (c * t - 1 + exp(-c * t))
  err = h - 2 m
END
solve(err,c)


# Example 13.18
MKS(deg)
v0 = 3 m/s
HH = 0.2 m
len = 0.12 m
hh = 0.06 m
BEGIN
  q = 45 deg
  x = v0^2 * sin(q)^2 - 2 * grav() * (HH - hh - len * sin(q))
  t1 = (v0 * sin(q) + sqrt(x)) / grav()
  t2 = (v0 * sin(q) - sqrt(x)) / grav()
  xe = len * cos(q) + v0 * cos(q) * t1
  xs = len * cos(q) + v0 * cos(q) * t2
  err = xe - xs
END
max(err,q)

# Homework Problems:

TBD