A cheetah and a gazelle are grazing in the savannah. The gazelle is 275 meters away from the gazelle safe zone and the cheetah is 455 meters away. If the gazelle can run at 25 m/s and the cheetah can run at 65 m/s will the gazelle get to safety? If not how fast does the gazelle need to run to beat the cheetah by 2 seconds? I

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

15.3 cos 65 degrees trig