Answer:
1) Yes, the gazelle gets to safety
2) The speed with which the gazelle needs to run, to beat the cheater by 2 seconds is approximately 29.79 m/s
Explanation:
1) The distance of the gazelle, from the gazelle safe zone = 275 m
The distance of the cheetah from the gazelle = 455 m
The speed of the gazelle = 25 m/s
The speed of the cheetah = 65 m/s
Therefore, we have;
Let the time the gazelle reaches the safe zone = t, which gives;
t = 275 m/(25 m/s) = 11
t = 11 seconds
Let the time the cheetah reaches the gazelle = t₁, we have;
455 + 25 × t₁ = 65 × t₁
t₁ = 455/40 = 11.375
t₁ = 11.375 seconds
The gazelle reaches the gazelle safe zone before the cheetah reaches the gazelle
Therefore, the gazelle gets to safety
2) In order for the gazelle to beat the gazelle by 2 seconds, we have;
The time for the cheetah to reach the safe zone = (275 + 455)/65 = 11.23 seconds
Therefore, we have;
In order for the gazelle to beat the gazelle by 2 seconds the time the cheetah reaches the safe zone = 11.23 - 2 = 9.23 s
The speed of the gazelle is then 275/9.23 ≈ 29.79 m/s
