
242 Forensic Engineering Fundamentals
In the earlier equations, g is the acceleration due to gravity, t is the time, and θ is the
angle of departure of the projectile relative to the reference plane. Equations 9.22 and
9.23 produce the trajectory in terms of time t. Eliminating t from the earlier equations,
we obtain
zx
gx
v
=−tan
cos
θ
θ
2
2
(9.24)
Equation 9.24 can be solved for the departure velocity given by
v
gx
0
2
2
2
=
−cos(ta
(9.25)
A special case of projectile motion occurs when an object falls freely. In terms of the coor-
dinate system utilized in the previous discussion, Equation 9.12 may be written as
zz vt at=+ +
00
1
2
(9.26)
but z
0
= v