Answer :
Final answer:
The cheetah will catch the gazelle in approximately 14.06 seconds.
Explanation:
To find out how long it takes for the cheetah to catch the gazelle, we need to calculate the time it takes for the cheetah to cover the distance between them. The gazelle is 80.1 meters ahead of the cheetah. Given that the cheetah's maximum speed is 97.4 km/h and the gazelle's maximum speed is 76.9 km/h, we can determine the time by dividing the distance between them by the difference in their speeds.
Difference in speeds = 97.4 km/h - 76.9 km/h = 20.5 km/h
Convert the difference in speeds to meters per second:
Difference in speeds = 20.5 km/h x 1000 m/km x (1/3600) h/s = 5.6944 m/s
Time = Distance / Speed = 80.1 m / 5.6944 m/s = 14.06 s
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Answer:
To find out how long it takes for the cheetah to catch the gazelle, we need to determine the time it takes for the cheetah to cover the 80.1 m distance between them.
First, let's convert the speeds from km/h to m/s for consistency. We can do this by multiplying the speeds by 1000/3600 (since there are 1000 meters in a kilometer and 3600 seconds in an hour).
The cheetah's speed in m/s is (97.4 km/h) * (1000 m/km) / (3600 s/h) = 27.0556 m/s.
The gazelle's speed in m/s is (76.9 km/h) * (1000 m/km) / (3600 s/h) = 21.3611 m/s.
Now, we can calculate the time it takes for the cheetah to cover the distance of 80.1 m. We can use the formula:
time = distance / speed.
Plugging in the values, we get:
time = 80.1 m / (27.0556 m/s - 21.3611 m/s) = 80.1 m / 5.6945 m/s = 14.05 seconds.
Therefore, it will take approximately 14.05 seconds for the cheetah to catch its prey.
explanation of why we did the subtraction of the two speeds:
By subtracting the gazelle's speed from the cheetah's speed, we can determine how much faster the cheetah is compared to the gazelle.
In this scenario, the cheetah needs to overcome the initial distance of 80.1 m between itself and the gazelle. The relative speed between the two animals determines how quickly the cheetah can close this gap.
By calculating the time it takes for the cheetah to cover the distance with the relative speed, we can determine how long it will take for the cheetah to catch up to the gazelle.
