1. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Lecture Notes Animals Cheetah Chase

2. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Physics: To solve a problem involving constant acceleration and constant motion. Biology: Learn about speed and acceleration characteristics of cheetahs and Thomson’s gazelles. Falling Cats Goals

3. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia 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. Cheetah Chase Big Ideas

4. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Gazelle vs Cheetah [4] [2] Cheetah [1] Max speed: 110 km/h (30.6 m/s) Acceleration 0 – 96 km/h in 3.0 s! (8.9 m/s 2 ) Catching prey should be easy, right? Gazelle [2,3] Max speed: 70 km/h (19.4 m/s) Acceleration: a g ~ 4.5 m/s 2 Can make sharp turns Good endurance

5. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Cheetah Chase Question 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?

6. Physics and Astronomy Outreach Program at the University of British Columbia 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.

7. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Cheetah Chase Visualization d c1 d c2 = 400 m d g2 ABCD 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. E Answer is the distance from A to C. d g1

8. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Cheetah Chase Strategy 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.

9. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Cheetah Chase Calculations Cheetah accelerates for time t c1 Distance travelled in time t c1 Cheetah acceleration phase :

10. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Cheetah Chase Calculations Cheetah travels at top speed for time t c2 Total time taken from start to finish Cheetah constant velocity phase : Total distance cheetah travelled

11. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Cheetah Chase Calculations Gazelle accelerates for time t g1 Distance travelled in time t g1 Gazelle acceleration phase :

12. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Cheetah Chase Calculations Gazelle travels at top speed for time t g2 Gazelle constant velocity phase : Total distance gazelle travelled Gazelle travels distance d g2 in time t g2

13. Physics and Astronomy Outreach Program at the University of British Columbia Cheetah Chase Calculations Distance gazelle ahead of cheetah : d c1 d c2 = 400 m d g2 ABCDE d g1

14. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Cheetah Chase Conclusions 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].

15. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Cheetah Chase Bibliography [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/Cheetahhttp://en.wikipedia.org/wiki/Cheetah [5] http://www.lioncrusher.lunarpages.com/animal.asp?animal=44