How Far Can a Jetliner Travel West Against a Jet Stream and Return Safely?

[confounded]

Homework Statement

A jetliner can fly 7.35 hours on a full load of fuel. Without any wind it flies at a speed of 3.42 x 10^2 m/s. The plane is to make a round-trip by heading due west for a certain distance, turning around, and then heading due east for the return trip. During the entire flight, however, the plane encounters a 43.3-m/s wind from the jet stream, which blows from west to east. What is the maximum distance (in kilometers) that the plane can travel due west and just be able to return home?

Homework Equations

I'm not sure, but I'm guessing this: d/s + d/s = overall time and... probably something else?

The Attempt at a Solution

Well, I assumed because the jet stream is traveling in the same direction as the plane in both directions (west and east) that 43.3 m/s would be added to 3.42 x 10^2 m/s for the speed of the plane going to and coming back. I also converted 7.35 hours to seconds. So I ended up with distance traveled west/385.3 + distance traveled east/385.3= 26,460 s. Afterward, I ended up with distance traveled west=10,195,038m-distance traveled east. Now I'm just completely lost/confused. I just started taking physics last week, so I'm pretty new at this and I probably did everything wrong. Please help!

(P.S. Should I make the distance traveled east negative, since it's going in the opposite direction?)

 

[HallsofIvy]

Homework Statement

A jetliner can fly 7.35 hours on a full load of fuel. Without any wind it flies at a speed of 3.42 x 10^2 m/s. The plane is to make a round-trip by heading due west for a certain distance, turning around, and then heading due east for the return trip. During the entire flight, however, the plane encounters a 43.3-m/s wind from the jet stream, which blows from west to east. What is the maximum distance (in kilometers) that the plane can travel due west and just be able to return home?

Homework Equations

I'm not sure, but I'm guessing this: d/s + d/s = overall time and... probably something else?

The Attempt at a Solution

Well, I assumed because the jet stream is traveling in the same direction as the plane in both directions (west and east) that 43.3 m/s would be added to 3.42 x 10^2 m/s for the speed of the plane going to and coming back.

Where did you get the idea that "the jet stream is traveling in the same direction as the plane in both directions"? The problem itself tells you that the jet stream "blows from west to east, while the airplane is flying, first, from east to west and then from west to east.

I also converted 7.35 hours to seconds. So I ended up with distance traveled west/385.3 + distance traveled east/385.3= 26,460 s. Afterward, I ended up with distance traveled west=10,195,038m-distance traveled east. Now I'm just completely lost/confused. I just started taking physics last week, so I'm pretty new at this and I probably did everything wrong. Please help!

(P.S. Should I make the distance traveled east negative, since it's going in the opposite direction?)

You are wrong to assume you should always add the speed of the jet stream. Going West the jet stream is opposing flight and must be subtracted.

 

[confounded]

Where did you get the idea that "the jet stream is traveling in the same direction as the plane in both directions"? The problem itself tells you that the jet stream "blows from west to east, while the airplane is flying, first, from east to west and then from west to east.


You are wrong to assume you should always add the speed of the jet stream. Going West the jet stream is opposing flight and must be subtracted.

Okay, I was thinking that the jet stream blew west, and THEN blew east...for some reason. Excuse me. So, (I mean...I'm guessing I set up my equation correctly...) it's distance traveled west/385.3 + distance traveled east/298.7 = 26,460s ? Then I solve for distance traveled west?

 

[HallsofIvy]

Yes, and since you know "distance traveled west"= "distance traveled east" that should be easy.

(Unfortunately, the jet stream isn't accomodating enough to change directions with the airplane!)

 

[confounded]

Yes, and since you know "distance traveled west"= "distance traveled east" that should be easy.

(Unfortunately, the jet stream isn't accomodating enough to change directions with the airplane!)

Okay, thank you so much!