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Answer :
Final answer:
The cheetah catches the gazelle in approximately 19.27 seconds. The minimum distance the gazelle must be ahead of the cheetah is 772.5 meters.
Explanation:
To determine the time it takes for the cheetah to catch up to the gazelle, we can use the formula:
time = distance/speed.
The distance the cheetah needs to cover is the initial distance between them minus the distance covered by the gazelle while the cheetah catches up. The time it takes for the cheetah to catch up to the gazelle is approximately 19.27 seconds.
To calculate the minimum distance the gazelle must be ahead of the cheetah to have a chance of escape, we need to find the distance covered by the cheetah in 7.5 seconds.
Using the formula distance = speed x time, we find that the cheetah covers a distance of 772.5 meters in 7.5 seconds.
Therefore, the minimum distance the gazelle must be ahead is 772.5 meters.
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Answer:
1
[tex] t_a = 13.49 \ s [/tex]
2
The distance is [tex] D = 55.2 \ m [/tex]
Explanation:
From the question we are told that
The maximum speed of the cheetah is [tex]v = 103 \ km/h = 28.61 \ m/s[/tex]
The maximum of gazelle is [tex]u = 76.5 \ km/h = 21.25 \ m/s[/tex]
The distance ahead is [tex]d = 99.3 \ m[/tex]
Let [tex]t_a[/tex] denote the time which the cheetah catches the gazelle
Gnerally the equation representing the distance the cheetah needs to move in order to catch the gazelle is
[tex] v* t_a = d + u* t_a [/tex]
=> [tex] 28.61 t_a = 99.3 + 21.25t_a [/tex]
=> [tex] 7.36 t_a = 99.3 [/tex]
=> [tex] t_a = 13.49 \ s [/tex]
Now at t = 7.5 s
[tex]7.5 v = D+ 7.5u [/tex]
=> [tex] 28.61 * 7.5 = D + 21.25* 7.5 [/tex]
=> [tex] 7.36 * 7.5 =D [/tex]
=> [tex] D = 55.2 \ m [/tex]
Hence the for the gazelle to escape the cheetah it must be 55.2 m
