Chapter 1.3, Problem 34E

To determine

To explain: if the statement, “if cheetah is 650 feet behind the antelope, then antelope is not safe”.

Answer to Problem 34E

No

Explanation of Solution

Given:

Speed of cheetah = 90 feet per second

Speed of antelope = 60 feet per second

Initial distance between Cheetah and antelope = 650 feet

Formula Used:

  $\text{Distance}=\text{speed}\times \text{time}$

Let the time taken by cheetah to catch up to the antelope be x seconds.

The distance travelled by Cheetah in x seconds $=90x$

The distance travelled by Antelope in x seconds $=60x$

As, in x seconds Cheetah catches up to antelope, so,

  $\begin{array}{c}90x-60x=650\\ 30x=650\\ x=\frac{650}{30}\\ x=21.67\end{array}$

But it is known that cheetah can run at its top speed only for 20 seconds and in the given case it requires 21.67 seconds for cheetah to catch up to antelope, so it can be said that the antelope will be safe.

Conclusion:

No, if the distance between them is 650 feet, then the antelope will be safe.