CE 3102
Fall, 2008
Thought Problem 2
Those of you who’ve taken CE 3201 might recall that traffic engineers get considerable use out
of the stopping distance equation:
g
V
VT
D
μ
2
2
+
=
D = stopping distance (feet),
V = vehicle speed (feet/second)
T = driver’s perception/reaction time (seconds),
μ
= coefficient of tire/pavement friction (dimensionless)
g = gravitational acceleration=32.2 feet/second
2
To simplify things, we’ll assume that driver reaction times can be 1, 2, or 3 seconds,
that vehicle
speeds can be 20, 40, 60, or 80 feet/second, and that μ=0.7.
Question 1
Sketch the sample spaces for V and T. Identify the following events graphically on the sketch.
a.
E = T > 2.0
e. I =
F
E
∪
b.
F =
V
≥
36
f. J =
(
)
F
E
∪
c.
G =
E
g. K= D > 100 feet
d.
H =
F
E
∩
Question 2
Based on spot a speed study and some human factors research, suppose we can assign the
following probabilities to each of the possible joint events:
V=
20
40
60
80
1
.05
.2
.2
.05
T=
2
.03
.09
.12
.06
3
.02
.04
.08
.06
a.
Do the numbers in this table represent a valid assignment of probabilities?
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 Spring '11
 Harshad number, 3 seconds, 80 feet, 36 g, 25 mph, 32.2 feet

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