Graphics Programs Reference
In-Depth Information
Practice Set C
DevelopingYour
MATLABSkills
Remarks.
Problem 7 is a bit more advanced than the others. Problem 11a
requires the Symbolic Math Toolbox; the others do not. SIMULINK is needed
for Problems 12 and 13.
1. Captain Picard is hiding in a square arena, 50 meters on a side, which is
protected by a level-5 force field. Unfortunately, the Cardassians, who are
firing on the arena, have a death ray that can penetrate the force field.
The point of impact of the death ray is exposed to 10,000
illumatons
of
lethal radiation. It requires only 50 illumatons to dispatch the Captain;
anything less has no effect. The amount of illumatons that arrive at point
(
x
,
y
) when the death ray strikes one meter above ground at point (
x
0
,
y
0
)
is governed by an inverse square law, namely
10
,
000
4
π
((
x
−
x
0
)
2
+
1)
.
+
(
y
−
y
0
)
2
The Cardassian sensors cannot locate Picard's exact position, so they fire
at a random point in the arena.
(a) Use
contour
to display the arena after five random bursts of the
death ray. The half-life of the radiation is very short, so one can
assume it disappears almost immediately; only its initial burst has
any effect. Nevertheless include all five bursts in your picture, like
a time-lapse photo. Where in the arena do you think Captain Picard
should hide?
(b) Suppose Picard stands in the center of the arena. Moreover, suppose
the Cardassians fire the death ray 100 times, each shot landing at
a random point in the arena. Is Picard killed?
(c) Rerun the “experiment” in part (b) 100 times, and approximate the
probability that Captain Picard can survive an attack of 100 shots.
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