Vector Situation: Find Shortest Time A to B (1000km)

[luysion]

Homework Statement

A plane is traveling from City A to City B which is 1000km due NORTH of city A. The plane has a maximum speed of 250km/hr in still air. If a wind is blowing due east at 150km/hr what is the shortest time for the plane to complete the journey A to B (in hours)
a)3.4
b)4.0
c)5.0
d)6.7
e)10.0

Homework Equations

The Attempt at a Solution

Ok so i got 3.4 (A) and i got this by constructing the triangle with the hypotenuse being the new resultant speed then using pythagoras. BUT my demononstrator said that 5.0 is the answer and that my triangle is incorrect I am really confused as to why can someone please help me clear this up!
cheers!

 

[Redsummers]

Well, first of all you should see that 3.4 is an absurd result because it's less than the time it would take if there was no wind, and in fact there's wind blowing to the east which is not helping to the trajectory whatsoever.
I guess your problem with the triangle was that you were assuming it to be a triangle rectangle?

 

[xcvxcvvc]

Homework Statement

A plane is traveling from City A to City B which is 1000km due NORTH of city A. The plane has a maximum speed of 250km/hr in still air. If a wind is blowing due east at 150km/hr what is the shortest time for the plane to complete the journey A to B (in hours)
a)3.4
b)4.0
c)5.0
d)6.7
e)10.0

Homework Equations

The Attempt at a Solution

Ok so i got 3.4 (A) and i got this by constructing the triangle with the hypotenuse being the new resultant speed then using pythagoras. BUT my demononstrator said that 5.0 is the answer and that my triangle is incorrect I am really confused as to why can someone please help me clear this up!
cheers!

You're on the right track to use a triangle, but you've set it up incorrectly as your demonstrator said. If wind is blowing east, the airplane must point itself into the oncoming wind to cancel out its eastward force, resulting in a single vector pointing straight toward north. If you draw this triangle, you see the airplane's velocity is actually the hypotenuse and is not a leg of the triangle.