January 26, 2006
1
Engineers 1
Spring Semester 2006
Lecture 8
January 26, 2006
2
Aquathlon
Aquathlon
(1)
(1)
!
The Aquathlon consists of two legs, a swim (distance b)
followed by a run (distance a).
a =
3 km,
b
= 1.5 km
!
The athletes swim with a speed
v
1
= 3.5 km/h
and run with a speed
v
2
= 14 km/h
Which angle
!
will result in the shortest finish time?
!
1) Red dashed line: shortest distance between start and
finish
a
2
+
b
2
=
1.5
2
+
3
2
km
=
3.354 km
January 26, 2006
3
3) Arbitrary path between those two
extremes: characterized by angle
!
Swim a distance of and then run a distance of
!
The total time is
Aquathlon(2)
Aquathlon(2)
Corresponding time
t
red
=
a
2
+
b
2
/
v
1
=
(3.354 km)/(3.5 km/h)
=
0.958 h
a
1
2
+
b
2
a
2
2) Swim straight to shore and
then run
t
blue
=
b
v
1
+
a
v
2
=
1.5 km
3.5 km/h
+
3km
14 km/h
=
0.643h
t
(
"
)
=
a
1
2
+
b
2
v
1
+
a
2
v
2
=
b
v
1
cos
+
a
#
a
1
v
2
=
b
v
1
cos
+
a
#
b
tan
v
2
January 26, 2006
4
Aquathlon(3)
Aquathlon(3)
t
(
)
=
b
v
1
cos
+
a
#
b
tan
v
2
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5
Aquathlon
Aquathlon
(4)
(4)
!
To find the minimum time
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 Spring '08
 Wolf
 Physics, Cartesian Coordinate System, Force

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