Sally is standing at one corner of a snowy rectangular field that measures 200 ft by 200 ft. She wishes toreach a warm cabin located at the diagonally opposite corner of the field. Suppose Sally trudges throughthe snow at 3 ft/sec to reach pointPat the other side of the field, and then walks the remaining distance along a paved road at 5 ft/sec to reach the cabin. What is the optimal point that will allow Sally toreach the cabin as quickly as possible

Complete Question

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The optimal point(i.e the position of  P) that will allow Sally to reach the cabin as quickly as possible is   from the cabin.

Step-by-step explanation:

From the question we are told that

   The speed from the point Sally is standing to the point P is  

   The speed from the point P to the cabin is

Let denote the distance from the bottom left corner to the  P  be  y  ft

 Generally according to Pythagoras theorem the distance from Sally's first position to point P is mathematically represented as

Generally the distance from that point P to the cabin is mathematically represented as

Generally the time it takes Sally to cover that distance s is mathematically represented as

=>    

Generally the time it takes Sally to cover that distance d is mathematically represented as

=>    

So the total time taken is  

Generally the minimum time taken with respect to the distance is mathematically evaluated by differentiating and equating the derivative to 0

So  

=>

=>        

=>          

=>

So the distance from point P to the cabin is  

=>      

So  the optimal point(i.e the position of  P) that will allow Sally to reach the cabin as quickly as possible is   from the cabin

29 is the correct answer

step-by-step explanation:

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