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CHAPTER 8
Topic AK-8
8.1 PROJECTILE MOTION ANALYSES WITH QUADRATIC AIR
RESISTANCE
A projectile of mass m is launched with an initial velocity v
0
at an initial launch angle of θ to the horizontal in the
uniform gravitational eld g (Figure 8.1). Ignoring the lift force determine variations of simulated projectile tra-
jectories with drag coecient, initial velocity, initial launch angle, and mass of the projectile both analytically (with
approximation) and numerically.
e following parameters are given in the table below: projectile’s mass m, density ρ, launch angle θ, reference area
(usually the face area) A, drag coecient C
D
, and initial launch velocity v
0
.
No.
m ρ θ A CD v
0
Verying
Parameter
g g cm
-3
deg cm
2
- m/s
1 10 7.86 15; 30; 45 2.5 1.5 900
θ
2 5; 10; 20 7.35 30 3.0 1.4 800
m
3 15 8.31 45 2; 3; 5 1.55 850
A
4 20 8.56 15 3.5 1.5; 2; 2.5 870
C
D
5 25 7; 8; 8.5 30 2.7 2.0 780
ρ
6 20 7.32 60 3.4 1.8 700; 800; 900
v
0
7 18 6.87 10; 25; 45 2.8 1.75 850
θ
8 15; 20; 30 7.98 35 4.0 1.43 740
m
9 22 7.23 45 3; 5; 8 1.85 880
A
10 34 7.65 25 5.5 1.3; 1.5; 2 815
C
D
11 29 7; 7.5; 8 35 4.7 1.55 820
ρ
12 38 8.3 40 5.2 1.46 600; 750; 800
v
0
13 45 7.9 20; 30; 45 4.7 1.57 950
θ
14 15; 25; 40 8.25 25 4.6 1.56 880
m
15 35 7.99 38 4; 5; 7 1.45 650
A
16 18 8.22 30 6 1.4; 1.8; 2.1 875
C
D
17 25 7.5; 8; 9 45 7 1.53 970
ρ
18 48 7.4 55 4.5 1.41 700; 800; 960
v
0
19 15 7.76 10; 25; 40 4.8 1.43 880
θ
20 25; 45; 60 8.32 35 6.5 1.65 920
m
21 45 7.54 32 3; 5; 7 1.60 870
A
22 40 6.99 25 4 1.3; 1.6; 2.1 950
C
D
23 35 6.8; 7; 8 42 5.8 1.44 875
ρ
24 24 7.76 45 5 1.53 750; 850; 950
v
0
25 18 7.68 20; 35; 60 6.2 1.46 780
θ
26 15; 35; 50 7.46 60 4.3 1.48 900
m
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