From rest, the cheetah can accelerate at 8.8 m/s2 and reach a top speed of 30 m/s (108 km/h)! It can maintain this maximum speed over a distance of about 400 meters before it needs to stop. On the other hand, the Thomson’s gazelle has a top speed of 70 km/h, which is less than the cheetah’s, but it can maintain this top speed for a while as well. From rest, the gazelle can accelerate at 4.5 m/s2 to reach its top speed.
From rest, the cheetah can accelerate at 8.8 m/s2 and reach a top speed of 30 m/s (108 km/h)! It can maintain this maximum speed over a distance of about 400 meters before it needs to stop.
On the other hand, the Thomson’s gazelle has a top speed of 70 km/h, which is less than the cheetah’s, but it can maintain this top speed for a while as well. From rest, the gazelle can accelerate at 4.5 m/s2 to reach its top speed.
When a cheetah goes after a gazelle, success or failure is a simple matter of
You will apply basic kinematics and simple assumptions to determine how a chase can play out.
The Scene:
A cheetah has spotted a gazelle. At the same instant the cheetah leaps into action, the gazelle has spotted him and starts heading directly away.
Q1. After what total distance from rest must the cheetah stop?
(clearly show calculations and substitutions)
Q2. In the elapsed time that the cheetah started and must stop, what distance can the gazelle cover?
(again clearly show your calculations and substitutions)
Q3. What is the maximum distance away from a gazelle a cheetah has to be initially, in order for the cheetah to have a chance of catching up to the gazelle?
(Hint: what would be the positions of the animals at the time when the cheetah must break off the chase?)
Your solution should include a completely labelled diagram for each animal showing its motion.
You have to clearly state any assumptions you made, and show the derivations and calculations and as usual, explain in complete sentences your steps. Note: in this problem, it’s not necessary to set equations for each animal equal to each other.
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