
253Trajectories
Once again, the prime symbol represents differentiation with respect to x, and Equations
8.121 and 8.122 are identical to those developed for the zero wind case. Now we have
already solved differential Equations 8.121 and 8.122 under their previous guise with the
result of
VV
xx
x
=−
∫
0
1
0
exp
ˆ
D
*
d
(8.124)
VCxV
g
V
Cx
y
x
y
x
x
x
=−
−
∫∫∫
ex
xp
*
d
*
d
1
00
1
0
0
2
dx
2
(8.125)
Equation 8.123 is somewhat more difcult to solve. It is a rst-order, linear differential
equation of the form y΄ + P(x)y = Q, whose solution, after the necessary integrations and
substitution of initial conditions that at x = 0, V
z
= 0, is ...