
and then integrating to obtain s
p
(t), the distance traveled by the projectile
s
p
(t) ¼
ð
t
0
v
p
(0)e
(m=m)t
dt (7:42)
¼
m
m
v
p
(0)[1 e
(m=m)t
], t 0 (7:43)
Setting s
p
(t
f
) ¼L and solving for t
f
give
t
f
¼
m
m
ln 1
mL
mv
p
(0)
¼
2000=32:2
0:1
ln 1
0:1(5000)
(2000=32:2)45(5280=3600)
¼ 80:79 s(7 :44)
There are a number of system parameters that can be varied to study their effect on the optimum
firing angle. Su ppose we wish to investigate the relationship between u
opt
and the target ’s speed v
T
.
The M-file ‘‘Chap7_opt_theta_vT.m’’ sequences through a range of target speeds v
T
¼5, 15, 25, . . . ,
65, 75 mph and finds the optimum firing angle for each speed. The result is shown ...