Answer:
Option A
The first route will be shorter
Explanation:
Considering the motion when the airline heads westward, the north direction speed is given by
[tex]N=\sqrt 260^{2}-40^{2}=257 m/s[/tex]
Distance to destination is 1500 Km= 1500000 m
Time for travelling=1500000/257=5836.58 seconds
Time in minutes=5836.58/60=97.3 minutes
In case the wind sends pilot off the course
Time to travel from A to point E before heading to Duluth=1500000/260=5769.23 seconds
Time in minutes=5769.23/60=96.2 minutes
Time to travel from Westward to Duluth=Distance/speed
Distance between Westward and Duluth=40*5769.23=230769.23 m
Time to travel from Westward point to Duluth=23769.23/(260-40)=1048.95 seconds
Time in minutes=1048.95/60=17.5 minutes
Total time taken when pilot changes course=96.2+17.5=113.7 minutes
Time difference=113.7-97.3=16.4 minutes
Therefore, the first route will be shorter .
Answer:
A) The first route will be shorter
Explanation:
Speed = [tex]\frac{Distance}{Time}[/tex]
The total distance to be covered in each case is 1500 Km= 1500000 m.
Heading westward, her air speed = 260 m/s.
So that the time required to cover the distance at that speed would be;
Time = [tex]\frac{Distance}{Speed}[/tex]
= [tex]\frac{1500000}{260}[/tex]
= 5769.231 seconds
But if she flies directly north, a blowing wind reduces her speed. Thus speed due north, [tex]S_{N}[/tex] is given by;
[tex]S_{N}[/tex] = [tex]\sqrt{260^{2} - 40^{2} }[/tex]
= 256.91 m/s
Time for traveling = [tex]\frac{Distance}{Speed}[/tex]
= [tex]\frac{1500000}{256.91}[/tex]
= 5838.621 seconds
Thus comparing the time of travel in both cases, the first route would be shorter .
