Environmental Engineering Reference
In-Depth Information
For the self-adhering impact
e
t
=
1, expression of
v
t
+
and ω
+
is simplified:
⎤
⎥
+
−
v
=−
e v
n
n
n
⎥
⎥
3
4
+
−
−
v
=
v
+
r
ω
[4.16]
⎥
⎥
⎥
t
t
7
7
−
v
r
10
3
+
−
t
ω
=
−
⎥
⎦
ω
7
7
Figure 4.6.
Oblique impact on a terrain with slope
β
4.4.
Flight trajectory
By neglecting the air resistance, the equations of movement of a material point
provides results for a boulder starting from a point of impact with a velocity
v
0
inclined at an angle α
on the horizontal (see Figure 4.7):
g
2
yxtg x
=
α
−
[4.17]
22
2 s
v
α
0
For a terrain with a constant slope β, for which the equation
y
= -
x tg
β, we easily
find the length of the jump
s
,
measured parallel to the slope, and the maximum flight
height
f
above the terrain (reached at half of
s
):
22
2 s
cos
v
α
(
)
s
=
tg
αβ
+
tg
[4.18]
g
β