When will a plane trip take more time when there is a wind or when there is no wind?

Question

I can't seem to figure out which one is right, i need help with this multiple question.

An airplane starts from A and goes to B at a
constant speed. After reaching B it returns
to A at the same speed. There was no wind.
Now, assume there was a wind from A to B of
constant magnitude.
Assume: The wind speed is less than that
of the plane (i.e., in magnitude).
When will the round trip take more time
when there is a wind or when there is no
wind?

1. Time taken is more when there is constant
wind.

2. Same in both cases because one way the
wind helps you and the other way it troubles
you.

3.Insufficient data.

4. Time taken is more when there is no
wind.


Thank you very much for your help.

Answer 1

This is a tricky question, and in fact, it is often used as part of a trick question. People are inclined to believe that the wind won't make a difference because it adds speed to you in one direction for a certain distance and reduces your speed by the same amount for an equal distance. However, distance is not what matters here. Time is what matters. Because the distance is fixed, you will spend more time on the slower leg of the journey and less time on the faster leg of the journey. Because you are traveling slower for a longer period of time, your average speed will be lower than your speed without wind.

For example, say you are flying 100 miles out and 100 miles back in a plane that does 100 mph. With no wind, the trip is one hour out and one hour back for a total of 2 hours. If you are flying into a 50 mile an hour wind, then your plane is only traveling 50 miles an hour in relation to the ground, and it will take you 2 hours just to travel 100 miles. Though the return trip will only take you 40 minutes traveling at 150 mph, your total trip time is going to clock out at 2h 40 min because of wind.

Your answer is number 1, and this same argument holds true for boats traveling against a current and all such similar circumstances.

Answer 2

I think it will take more time if there is wind.

Assume the distance between A and B is 200 miles.
You can travel at 150 mph with no wind.

Case 1: No wind
The total distance traveled would be 2(200)=400 miles
You travel at a constant speed of 150mph.
Distance = speed x time
time = Distance / speed
400/150 = 2.6666666666666667 hours

Case 2: With 20 mph wind blowing from A to B.
Your speed from A to B would be 150 + 20 = 170 mph.
To get from A to B, it would take 200/170 = 1.176470588 hours

Your speed from B to A would be 150 - 20 = 130 mph
To get from B to A, it would take 200/130 = 1.53846 hours.
The total time would be 2.7149 hours.

If you compare those time, it would take less without wind.

If you want to do it algebraically.
Wind speed = w
Normal speed of plane = v
Distance from A to B = x

Time w/ no wind = (2x)/v
Time with wind = x/(v+w) + x/(v-w)

Now you compare to see which one is greater.
(2x)/v ? x(v+v) + x/(v-w)

Find a common denominator on the right side, and you get:
(2x)/v ? (x(v-w)+x(v+w))/((v-w)(v+w))
(2x)/v ? x(v-w + v+w)/(v^2 - w^2)
(2x)/v ? x(2v)/(v^2-w^2)
1/v ? v/(v^2 - w^2) Multiply both sides by v^2- w^2 and v
v^2-w^2 ? v^2
-w^2 ? 0
<
Well, whatever value you let w be, the left side will always be less than 0. If there were no wind speed, it would be =, which means the time will be the same going there and coming back.
I hope this helps. :) Sorry if I made any typos, but you get the trend.

Answer 3

Theoretically, flying into the wind reduces the speed of the aircraft. This would cause the trip to take longer. While all of this makes for a nice theory discussion, on the practical side of commercial flight, it has little bearing. With all of the navigational aids, and flight times established, these factors are accounted for, and made as negligible as possible. The variables left out would be wind conditions at points of departure and arrival. A fast trip either way could become longer if the conditions at the airport are bad for any of a number of reasons. I know that you did not mention these, but they are points to consider.
#4 is out as an answer. On a practical side, if there is no wind, and the schedule of the aircraft is slow, the pilot could opt for a higher speed to catch up on lost time. #3 is out, there is sufficient data if one has experience to draw from. #1 is theoretically correct, but not on a practical situation. #2 appears to be based on averages, time lost flying into the wind is made up for with a tail wind.

Answer 4

Number 1 is correct. If the wind speed matches the plane's speed, it will take infinite time to go back from B to A, no matter how long it takes to go from A to B. So if it's just a little bit less than the plane's speed, it will take just a little less than eternity, but longer nevertheless.

Answer 5

the answer is extremely a lot less stressful then you absolutely ought to imagine. imagine of the wind as a consistent because the question would not say it changes. Now with that in ideas purely take the gap 800 miles and divide it via 5 having reported that via 8. 800/5=one hundred sixty miles an hour 800/8=one hundred miles an hour. now because the wind is consistent purely generic both figures to get the speed of the airplane with out the wind. (one hundred sixty+one hundred)/2=one hundred thirty miles an hour you understand the wind velocity is 30 because the form with out the wind is plus or minus 30 in preserving with no matter when you're antagonistic to it or with it. desire this helped :)

Answer 6

2. correct answer - FINAL ANSWER

When there is a wind - in the direction you are going
you add it 150 airspeed + 20 wind = 170 ground mph

on the return - it is subtracted 150-20 = 130 airspeed

however, since you had 20 + and 20- should equal out to
same time for the round trip - one leg quicker - one longer

Answer 7

no one mentioned that if you fly higher on one of the trips, the atmosphere is thinner, thus less drag, thus you fly faster, regardless of the wind speed.

(for your homework, #2 is correct)

Answer 8

It depends on which way the jet stream is going Faster when with you and more time when against you

Answer 9

with wind

Answer 10

THERE WOULDNT BE WIND ITS CALLED TURBULENCE....CAUSED BY OTHER AIRPLANES SO THAT TURBULENCE CAN MAKE YOUR AIRPLANE GO OUT OF CONTROL AND *BOOM*....