A cheetah can run at top speed for only about 20 seconds. if the cheetah running at 90 feet per second is 650 feet behind it. Is your friend correct?

Question

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 an antelope running 60 feet per second will not be safe if the cheetah running at 90 feet per second is 650 feet behind it. Is your friend correct?

Answer 1

Solve for the time it takes the cheetah to reach the moving antelope, and see if it exceeds 20 s.

 

Position of antelope at time t:

 

x = 650 + 60t

 

The cheetah must arrive at the same place at the same time:

 

x = 90t

 

650 + 60t = 90t

 

30t = 650

 

t = 650/30 ≅ 21.7 s

 

It takes the cheetah a little more than 20 s running at 90 ft/s to reach the moving antelope, so assuming the antelope can maintain its speed of 60, it is safe. The friend is not correct.

Answer 2

In the 20 second period, running at 90 ft/sec, the

cheetah runs:  20(90) = 1800 ft

 

The antelope runs 60 ft/sec for 20 sec = 60(20) = 1200 ft

in the same period.  Adding to this distance ran the initial

650 ft the antelope was ahead of the cheetah we have 1850 ft.

The antelope is still 50 ft ahead of the cheetah and is presumably

safe.  Your friend is NOT correct.