Kinematics Equations Video Lessons

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Problem: A cheetah spots a Thomsons gazelle, its preferred prey, and leaps into action, quickly accelerating to its top speed of 30 m/s, the highest of any land animal. However, a cheetah can maintain this extreme speed for only 15 s before having to let up. The cheetah is 290 m from the gazelle as it reaches top speed, and the gazelle sees the cheetah at just this instant. With negligible reaction time, the gazelle heads directly away from the cheetah, accelerating at 4.6 m/s2 for 5.0 s, then running at constant speed.Does the gazelle escape?

FREE Expert Solution

We'll consider the kinematic equations:

 vf = v0 +atx= (vf+v02)tx= v0t+12at2 vf2= v02 +2ax

Let both the cheetah and the gazelle be moving in the x-direction. 

The initial position of the cheetah, x0c = 0m

The initial position of the gazelle, x0g = 290 m

The cheetah accelerates to the top speed in no time. 

The velocity then remains constant in the entire path. 

vc = 30 m/s

The cheetah maintains the top speed for 15s.

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Problem Details

A cheetah spots a Thomsons gazelle, its preferred prey, and leaps into action, quickly accelerating to its top speed of 30 m/s, the highest of any land animal. However, a cheetah can maintain this extreme speed for only 15 s before having to let up. The cheetah is 290 m from the gazelle as it reaches top speed, and the gazelle sees the cheetah at just this instant. With negligible reaction time, the gazelle heads directly away from the cheetah, accelerating at 4.6 m/s2 for 5.0 s, then running at constant speed.

Does the gazelle escape?

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Kinematics Equations concept. You can view video lessons to learn Kinematics Equations. Or if you need more Kinematics Equations practice, you can also practice Kinematics Equations practice problems.

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Based on our data, we think this problem is relevant for Professor Deemyad's class at UTAH.