Animals
Cheetah Chase
Problem Set Solutions
Problem 1:
Cheetahs are the fastest land animal and can reach a top speed of approximately 110 km/h
within 3.4s [1]. Thomson’s gazelles, their favourite prey, can reach speeds of 70 km/h [2].
A. If a gazelle runs right past a stationary cheetah at top speed, how long would it take for
the cheetah to catch up with the gazelle?
B. How far did the cheetah have to run to catch up to the gazelle?
Ignore any lag of decision making time on the part of the cheetah, so that the moment the
gazelle passes the cheetah, the cheetah starts accelerating.
Solution 1A:
Calculations:
Initially, the cheetah is accelerating with constant acceleration where v f = 110 km/h =30.6 m/s,
vi = 0 km/h = 0 m/s, and  t = 3.4 s, giving a = 8.9 m/s2.
a
v f  vi
t

30.6m / s
 8.9m / s 2
3.4s
During the first 3.4 seconds the cheetah travels
dc 
v 2f  vi2
2a

30.6m / s
 52.5 m
(2)(8.9m / s 2 )
During the first 3.4 seconds the gazelle ( v g = 70 km/h = 19.4 m/s) travels
d g  v g t  (19.4m / s)(3.4s )  66.1m .
After the first 3.4 seconds, the gazelle is d  d g  d c  66.1m  52.5m  13.6m ahead and both
the cheetah and the gazelle are traveling constant velocity (uniform motion) with the cheetah
traveling (30.6 –19.4) m/s = 11.2 m/s faster than the gazelle. The time it takes in total for the
cheetah to catch up to the gazelle is (3.4s + d/ 11.2m/s) = 3.4 + (13.6m/11.2 m/s) = 4.6 s.
University of British Columbia Department of Physics and Astronomy
Solution 1B:
During the first 3.4 seconds the cheetah is accelerating and travels 52.5 m as we saw in part A.
For the remaining (4.6 – 3.4) s = 1.2 s until the cheetah catches up to the gazelle the cheetah is
travelling at a constant velocity of 30.6 m/s and will travel a distance of (30.6 m/s)(1.2 s) =
36.7m. In total the cheetah travels 89.2 m.
References:
[1] http://openlearn.open.ac.uk/mod/resource/view.php?id344455
[2] http://en.wikipedia.org/wiki/Thomson’s_Gazelle
Janelle Van Dongen 2009/08/17
University of British Columbia Department of Physics and Astronomy