The cheetah can maintain its maximum speed
for only 7.5 s.
What is the minimum distance the gazelle
must be ahead of the cheetah to have a chance
of escape? (After 7.5 s the speed of cheetah is
less than that of the gazelle.)
Answer in units of m
Well, the cheetah may be the fastest land animal, but even it needs some personal space. To determine the minimum distance the gazelle must be ahead to have a chance of escape, let's consider that after 7.5 seconds, the cheetah won't be zooming ahead like a rocket.
Now, I don't know exactly how fast these animals can sprint, but let's say the gazelle can maintain a constant speed of 15 m/s. In that case, after 7.5 seconds, the gazelle would have covered a distance of 7.5 s * 15 m/s = 112.5 meters.
Thus, if the gazelle wants to have a fighting chance of escape, it should be a considerable 112.5 meters ahead of the cheetah. Safety first!
To determine the minimum distance the gazelle must be ahead of the cheetah, we need to consider the relative speeds of both animals.
Let's assume the initial distance between the gazelle and the cheetah is 'd' meters. After 7.5 seconds, the cheetah can no longer maintain its maximum speed, while the gazelle continues to run at its usual speed.
The speed of the cheetah is denoted by 'C' meters per second, and the speed of the gazelle is denoted by 'G' meters per second.
Since the cheetah can only maintain its maximum speed for 7.5 seconds, the distance it can cover in that time is given by:
Distance covered by the cheetah = C * 7.5 meters
At the same time, the gazelle will have covered a distance of:
Distance covered by the gazelle = G * 7.5 meters
For the gazelle to have a chance of escaping, the distance covered by the cheetah should be less than the distance covered by the gazelle. Therefore, we can set up the following inequality:
C * 7.5 < G * 7.5
Simplifying the inequality by canceling out the common factor of 7.5, we have:
C < G
This inequality represents the condition where the speed of the cheetah is less than the speed of the gazelle. Now, let's solve for the minimum distance, 'd', by considering the condition C < G.
To have a chance of escape, the gazelle must be ahead of the cheetah by at least one stride length. In other words, the minimum distance the gazelle must be ahead is equal to the distance covered by the gazelle in one stride.
Therefore, the minimum distance 'd' is equal to G * 7.5 meters.
Answer: The minimum distance the gazelle must be ahead of the cheetah to have a chance of escape is G * 7.5 meters.
To find the minimum distance the gazelle must be ahead of the cheetah, we need to determine the maximum distance the cheetah can cover in 7.5 seconds based on its speed.
Let's assume the speed of the cheetah, S_c, and the speed of the gazelle, S_g.
Since the cheetah can maintain its maximum speed for only 7.5 seconds, the distance it can cover in that time is given by:
Distance_c = Speed_c × Time = S_c × 7.5
For the gazelle to have a chance of escape, the speed of the cheetah must be less than that of the gazelle after 7.5 seconds:
S_c < S_g
To determine the minimum distance the gazelle must be ahead, we need to find the distance the gazelle can cover during the 7.5 seconds.
Distance_g = Speed_g × Time = S_g × 7.5
The minimum distance the gazelle must be ahead of the cheetah is the difference between Distance_g and Distance_c, which gives:
Minimum Distance = Distance_g - Distance_c
= (S_g × 7.5) - (S_c × 7.5)
= 7.5 × (S_g - S_c)
So, the minimum distance the gazelle must be ahead of the cheetah to have a chance of escape is 7.5 times the difference in their speeds (S_g - S_c), measured in meters.
108km/hr = 108,000m/3600s= 30m/s
75.9km/hr = 75900m/3600s = 21.1m/s
the simplest way to do this is to recognize that the cheetah travels 8.9m/s faster than the gazelle
the cheetah has to make up a difference of 70.9 m with its speed advantage of 8.9m/s, so it will take the cheetah
time = dist/speed = 70.9m/8.9m/s = 8s
if the cheetah can maintain this speed advantage for only 7.5s, it can only close a distance of 8.9m/s x 7.5 s = 66.8m, so this is the minimum safety distance for the gazelle