# A plane travels from Detroit to Seattle WA and back (Seattle is to the West ofDetroit). In both trips the plane’s engines provide full power, giving the plane a speed of800 km/h relative to the surrounding air. During both trips there is uniform wind relativeto the ground with a velocity pointing toward the southeast at 45◦relative to the westeast axis. Assume the time spent for lift-off and landing maneuvers to be insignificant.Which of the following is correct?A) The trip from Detroit to Seattle takes more timeB) The trip from Seattle to Detroit takes more timeC) Both trips take the same timeD) Not enough information, we also need the to know the magnitude of the velocity ofthe wind

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A plane travels from Detroit to Seattle WA and back (Seattle is to the West of
Detroit). In both trips the plane’s engines provide full power, giving the plane a speed of
800 km/h relative to the surrounding air. During both trips there is uniform wind relative
to the ground with a velocity pointing toward the southeast at 45◦
relative to the westeast axis. Assume the time spent for lift-off and landing maneuvers to be insignificant.
Which of the following is correct?
A) The trip from Detroit to Seattle takes more time
B) The trip from Seattle to Detroit takes more time
C) Both trips take the same time
D) Not enough information, we also need the to know the magnitude of the velocity of
the wind

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Step 1

Consider vPA be the velocity of the plane with respect to surrounding air and vAG be the velocity of air with respect to the ground. The wind is blowing in south east direction and makes an angle 45 degree with respect east west direction.

Step 2

Draw the diagram. Here, D and S’ is the position of the Detroit and Seattle respectively.

Step 3

In the question, there are two components of the velocity of the wind with respect to ground. The one component of velocity vAG are along East while the other ...

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