Animals
Cheetah Chase
Lecture Notes
Physics and Astronomy Outreach Program at the University of British Columbia
Goals
Falling Cats
• Physics: To solve a problem involving
constant acceleration and constant
motion.
• Biology: Learn about speed and
acceleration characteristics of
cheetahs and Thomson’s gazelles.
Physics and Astronomy Outreach Program at the University of British Columbia
Big Ideas
Cheetah Chase
• Physics: During a chase animals go
through an initial acceleration phase
and a phase at which they can travel
at top speed.
• Biology: Cheetahs can maintain top
speed for a limited distance.
Physics and Astronomy Outreach Program at the University of British Columbia
Gazelle vs Cheetah
Cheetah[1]
Gazelle[2,3]
• Max speed: 110 km/h (30.6 m/s)
• Max speed: 70 km/h (19.4 m/s)
• Acceleration 0 – 96 km/h in 3.0 s!
• Acceleration: ag ~ 4.5 m/s2
(8.9 m/s2)
• Catching prey should be easy,
right?
• Can make sharp turns
• Good endurance
[4]
Physics and Astronomy Outreach Program at the University of British Columbia
[2]
Question
Cheetah Chase
Cheetahs can only keep up their maximum
speed for ~ 400 m, so they need to be
relatively close to their prey [5].
What is the maximum distance away from
a gazelle for a cheetah to have a chance
of catching the gazelle?
Physics and Astronomy Outreach Program at the University of British Columbia
Cheetah Chase
Assumptions
• The cheetah and gazelle start accelerating
at the same time.
• The rate of acceleration from rest to top
speed is constant.
• The gazelle only runs straight.
Physics and Astronomy Outreach Program at the University of British Columbia
Visualization
A
B
C
D
dg1
dc1
Cheetah Chase
E
dg2
dc2 = 400 m
• Cheetah starts at A, accelerates until B and
continues at top speed until E.
• Gazelle starts at C, accelerates until D and
continues at top speed until E.
• Answer is the distance from A to C.
Physics and Astronomy Outreach Program at the University of British Columbia
Strategy
Cheetah Chase
• Calculate the distance travelled and the
time taken for the cheetah to initially
accelerate and then travel 400 m.
• Calculate the distance the gazelle travelled
during this time.
• Find the difference between how far the
gazelle and the cheetah travelled.
Physics and Astronomy Outreach Program at the University of British Columbia
Calculations
Cheetah Chase
Cheetah acceleration phase :
Cheetah accelerates for time tc1
tc1 
v fc  vic
ac
(30.6  0) m s -1

 3.4 s
-2
8.9
ms
Distance travelled in time tc1
v 2fc
1 2
(30.6 m s )
d c1 

 52.5 m
2
2ac (2)(8.9 m s )
Physics and Astronomy Outreach Program at the University of British Columbia
Calculations
Cheetah Chase
Cheetah constant velocity phase :
Cheetah travels at top speed for time tc2
tc 2
dc2
400 m


 13.1 s
1
v fc 30.6 m s
Total time taken from start to finish
tc  tc1  tc2  3.4 s 13.1s 16.5 s
Total distance cheetah travelled
d c  d c1  d c 2  (400  52.5) m  452.5 m

Physics and Astronomy Outreach Program at the University of British Columbia
Calculations
Cheetah Chase
Gazelle acceleration phase :
Gazelle accelerates for time tg1
t g1 
v fg  vig
ag
(19.4  0) m s -1

 4.3 s
-2
4.5
ms
Distance travelled in time tg1
(19.4 m s 1 ) 2
d g1 

 42.0 m
2
2a g (2)(4.5 m s )
2
v fg
Physics and Astronomy Outreach Program at the University of British Columbia
Calculations
Cheetah Chase
Gazelle constant velocity phase :
Gazelle travels at top speed for time tg2
t g 2  t c  t g1  (16.5  4.3) s  12.2 s
Gazelle travels distance dg2 in time tg2

d g 2  vgf  t g 2  236.7 m
Total distance gazelle travelled
d g  d g1  d g 2  (42.0  236.7) m  278.7 m
Physics and Astronomy Outreach Program at the University of British Columbia
Calculations
Cheetah Chase
Distance gazelle ahead of cheetah :
A
B
C
D
dg1
dc1
E
dg2
dc2 = 400 m
d g  d g1  d g 2  278.7 m
d c  d c1  d c 2  452.5 m
d c  d g  (452.5 - 278.7) m  174 m
Physics and Astronomy Outreach Program at the University of British Columbia
Conclusions
Cheetah Chase
The gazelle could not possibly be caught
by the cheetah if the gazelle is more than
174 m ahead of the cheetah (assuming they
both start running at the same time.).
This assumes linear motion. In real life
gazelles use turning maneuvers to escape
and the cheetah will quietly come within 10-30
m and then initiate a chase [4].
Physics and Astronomy Outreach Program at the University of British Columbia
Bibliography
Cheetah Chase
[1] http://openlearn.open.ac.uk/mod/resource/view.php?id=344455
[2] http://en.wikipedia.org/wiki/Thomson's_Gazelle
[3] McNeill Alexander, “Principles of animal locomotion”, Princeton
University Press, p. 3, (2003)
[4] http://en.wikipedia.org/wiki/Cheetah
[5] http://www.lioncrusher.lunarpages.com/animal.asp?animal=44
Physics and Astronomy Outreach Program at the University of British Columbia