a cheetah can run at top speed for

Jaiden Mitchell

Jaiden Mitchell

Answered question

2022-08-28

a cheetah can run at top speed for only about 20 seconds .if an antelope is too far away for a cheetah to catch it in 20 seconds , the antelope is probably safe . your friend claims the antelope in exercise 33 will not be safe if the cheetah starts running 650 feet behind it . is your friend correct? explain 

Answer & Explanation

xleb123

xleb123

Skilled2023-06-03Added 181 answers

To determine whether the antelope is safe or not if the cheetah starts running 650 feet behind it, we need to consider the speeds of both animals and the distance between them.
Let's assume the cheetah's top speed is denoted by vcheetah and the distance between the cheetah and the antelope is denoted by d. The cheetah can run at its top speed for only about 20 seconds.
We can calculate the distance the cheetah can cover in 20 seconds using the formula:
dcheetah=vcheetah×t
Given that t=20 seconds, we have:
dcheetah=vcheetah×20
Now, let's determine whether the cheetah can reach the antelope in 20 seconds when it starts running from 650 feet behind.
The total distance the cheetah needs to cover is the distance between the cheetah and the antelope, which is d, plus the initial distance of 650 feet.
Therefore, the total distance the cheetah needs to cover is dtotal=d+650.
If the cheetah can cover this total distance dtotal within 20 seconds, then the antelope is not safe.
However, if dcheetah is less than dtotal, then the cheetah cannot catch the antelope in 20 seconds, and the antelope is safe.
So, the condition for the antelope to be safe is:
dcheetah<dtotal
Substituting the expressions for dcheetah and dtotal:
vcheetah×20<(d+650)
We know that the cheetah starts running 650 feet behind the antelope, so d=650. Substituting this value:
vcheetah×20<(650+650)
Simplifying:
vcheetah×20<1300
Now, let's analyze this inequality. Since the time is fixed at 20 seconds, the cheetah can only cover a limited distance. Therefore, for the antelope to be safe, the inequality must hold true. If the speed of the cheetah multiplied by 20 is less than 1300 feet, then the antelope is indeed safe.
If the cheetah's top speed multiplied by 20 is greater than or equal to 1300 feet, then the antelope is not safe, and your friend's claim is incorrect.

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