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A cheetah can run at 105 ft/s, but only for 7 seconds. The cheetah is at...

A cheetah can run at 105 ft/s, but only for 7 seconds. The cheetah is at (0,0) when it sees an antelope which is moving accoording to the parametric equation (x,y)= (-39+40t , 228+30t), where t is in seconds and (x,y) are measured in feet. If the cheetah started to run at t=0 it could catch the antelope. How many seconds can the cheetah afford to wait before starting? Assume that the cheetah does not change direction when it runs.

Expert Solution

Givent hat cheetah can run at 105 ft/s but only for 7 seconds.

So, within 7 seconds it has to catch the antelope. Cheetah runs in a straight line without changing the direction.

We have the co=ordinate for antelope run, (x,y)= (-39+40t , 228+30t)

at t=0, cheetah at (0,0) and antelope at (-39,228). The distance between two points is . implies, = 8892 ft distance. It can not catch the antelope.

at t =1, cheetah at 105 feet (if it runs) and antelope at (1,258) distance between two points is,

258 ft. It can not catch the antelope.

at t = 2, cheetah at 210 feet (if it runs) and antelope at (41,288). The distance between two points is ,

290.90ft. Cheetah can not catch the antelope.

at t=3 ,cheetah at 315 feet (if it runs) and antelope at (81,318). The distance between two points is

328.15ft. So, it can not catch the antelope.

at t = 4, cheetah at 420ft, and antelope at (121, 348).

The distance between two points is 368.43 ft.15ft. So, it can catch the antelope.

So, if cheetah starts at (0,0) and within 4 seconds it could catch the antelope.

But cheetah wants to wait for some time. So, let antelope runs for 7 seconds. Co-ordinates of antelope are,

(241, 438). The distance between origin and the point of antelope is 500 ft.

Cheetah can run this 500 ft in 4.76 seconds(525 ft in 5 seconds).

So, cheetah can wait for 2.238 seconds and can catch antelope which is in 500 ft distance.

milcah answered 2 years ago

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