Question

Cheetahs have been clocked at a top speed of approximately 102.6 ft/s. Gazelles are a main

part of a cheetah's diet. Gazelles have been clocked at a top speed of approximately 73.3 ft/s.
Suppose a cheetah sees a gazelle across the plains of Africa, 500 feet away, and begins to
run after it. The gazelle spots the cheetah and begins running at the same time the cheetah
does.
Determine how many seconds later the cheetah catches the gazelle. How many feet did the
cheetah have to run to catch the gazelle? Round to the nearest tenth of a foot. Show all your work.
DO NOT PUT ANY LINKS TO A FILE OR ANYTHING LIKE THAT. Help ASAP pls.

Answer 1

9514 1404 393

Answer:

• 17.1 seconds
• 1750.9 feet

Explanation:

The distance from the cheetah's starting point (in feet) can be modeled by ...

for the cheetah

c = 102.6t

for the gazelle

g = 73.3t +500

When these are equal, the cheetah will have caught the gazelle:

c = g

102.6t = 73.3t +500

29.3t = 500

t = 500/29.3 ≈ 17.1 . . . . . . seconds

The distance at that time is ...

c = 102.6(17.0648) ≈ 1750.9 . . . . feet

_____

Additional comment

The cheetah can maintain top speed only for about 10 seconds. At 500 ft distance, the gazelle is pretty safe.