how long before the cheetah gets its prey

Question

A cheetah can run at a maximum speed 103 km/h and a gazelle can run at a maximum speed of 76 km/h. If both animals are running at full speed, with the gazelle 84.1 m ahead, how long before the cheetah catches its prey

Answer 1

This problem explores the concept of relative speed.

 

1. Given:
2. You know your speeds and distance between the gazelle and cheetah. Knowing this, you know the relative speed of the cheetah with respect to the gazelle. You can use this relative speed to determine how long it would take the cheetah to gain on the gazelle knowing that the cheetah has to travel 84.1 m (pay careful attention to your units)
3. Unknown:
4. You want to solve for time (t)
5. Equations:
6. (1) V_cg (velocity of cheetah with respect to gazelle) = v_cheetah - v_gazelle
7. In this example, you want to consider the cheetah's speed relative to the gazelle. That is, consider both are moving in the positive direction; therefore, your relative speed would be v_cheetah - v_gazelle
8. (2) V_cg = Δx / Δt
9. (3) Δx = x_final - x_initial
10. If your cheetah is gaining on the gazelle, consider that the cheetah is moving at V_cg and that your gazelle is motionless. Moving at the relative speed, how long does it take your cheetah to travel 84.1 m?
11. Set-up:
12. Solve your 3 equations above for change in time.
13. Solve:
14. Pay careful attention to your units.
15. Plug in your values and find time (in hours) that it will take
16. Your answer will be less than 1 minute and more than 5 seconds.