Answer :
Final answer:
Given the Relative Speed of the cheetah and gazelle, and the initial distance between them, it would take about 17.79 seconds for the cheetah to catch up to the gazelle at their maximum speeds.
Explanation:
This problem relates to the concepts of relative speed and distance in physics. Relative speed is the speed of one object as observed from another. To find out how long the cheetah would take to catch the gazelle, we need to find the relative speed, which is the difference in speed between the two animals. In this case, the relative speed is 97.8 km/h (cheetah's speed) - 78.2 km/h (gazelle's speed), which equals 19.6 km/h, or approximately 5.44 m/s when converted.
Now we need to calculate the time it takes for the cheetah to traverse the initial distance between it and the gazelle, which is 96.8 m. This can be found using the formula: Time = Distance ÷ Speed. Using the data, we have: Time = 96.8 m ÷ 5.44 m/s, yielding approximately 17.79 seconds.
Therefore, it would take the cheetah about 17.79 seconds to catch up with the gazelle, assuming they both maintain their maximum speeds and start from the stated initial separation.
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