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.

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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 1 year ago

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