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Physics and Astronomy Outreach Program at the University of British Columbia

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.

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Physics and Astronomy Outreach Program at the University of British Columbia

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

  2. 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

  3. 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

  4. Gazelle vs Cheetah • Cheetah[1] • Max speed: 110 km/h (30.6 m/s) • Acceleration 0 – 96 km/h in 3.0 s! (8.9 m/s2) • Catching prey should be easy, right? • Gazelle[2,3] • Max speed: 70 km/h (19.4 m/s) • Acceleration: ag ~ 4.5 m/s2 • Can make sharp turns • Good endurance [4] [2] Physics and Astronomy Outreach Program at the University of British Columbia

  5. 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

  6. 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

  7. Visualization Cheetah Chase A B C D E dg1 dg2 dc1 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

  8. 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

  9. Calculations Cheetah Chase Cheetah acceleration phase : Cheetah accelerates for time tc1 Distance travelled in time tc1 Physics and Astronomy Outreach Program at the University of British Columbia

  10. Calculations Cheetah Chase Cheetah constant velocity phase : Cheetah travels at top speed for time tc2 Total time taken from start to finish Total distance cheetah travelled Physics and Astronomy Outreach Program at the University of British Columbia

  11. Calculations Cheetah Chase Gazelle acceleration phase : Gazelle accelerates for time tg1 Distance travelled in time tg1 Physics and Astronomy Outreach Program at the University of British Columbia

  12. Calculations Cheetah Chase Gazelle constant velocity phase : Gazelle travels at top speed for time tg2 Gazelle travels distance dg2in time tg2 Total distance gazelle travelled Physics and Astronomy Outreach Program at the University of British Columbia

  13. Calculations Cheetah Chase Distance gazelle ahead of cheetah : A B C D E dg1 dg2 dc1 dc2 = 400 m Physics and Astronomy Outreach Program at the University of British Columbia

  14. 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

  15. 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

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