The cheetah will catch the gazelle in approximately 11.57 seconds.
To determine how long it takes for the cheetah to catch the gazelle, we need to find the time it takes for the cheetah to cover the distance between them. We can calculate this time using the equation:
Time = Distance / Speed
The distance the cheetah needs to cover is the initial distance between the two animals plus the distance the gazelle travels in the same time it takes the cheetah to catch up. Given that the cheetah is 97.4 m behind and the gazelle and cheetah are traveling at their respective maximum speeds, we can calculate the time as follows:
Time = (97.4 m + Speed of gazelle × Time) / Speed of cheetah
Simplifying this equation, we get:
Time = 97.4 m / (Speed of cheetah - Speed of gazelle)
Now we can substitute the given values:
Time = 97.4 m / (101 km/h - 70.7 km/h)
Converting the speeds to m/s:
Time = 97.4 m / ((101 km/h - 70.7 km/h) × (1000 m/1 km) / (3600 s/1 h))
Simplifying further:
Time = 97.4 m / (30.3 km/h × (1000 m/1 km) / (3600 s/1 h))
Time = 97.4 m / (8.42 m/s)
Calculating this, we get:
Time ≈ 11.57 seconds
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