physics question

[261252]

A plane does a round trip with no wind

trip is 100 miles one way and it flies 100 mph so it takes 2 hours

then the same trip with a 50 mph headwind one way and the same backwind the other way

Do the trips take the same time or more time or less time?

 

[shack]

It depends how long it takes him to fly the 100 miles into the 50mph headwind.

If the 50 mph headwind slows him down 50%, then it takes him 2 hours just to do the 1st half of the trip which is what the total trip took with no wind. So it has to take more time with there being a wind.

I think we need to know how much the wind slowed him down to give a definitive answer.

 

[261252]

your reasoning is correct
while he goes 150 one way and 50 the other way plane spends more time going slow than fast

 

[Ponderling]

It is more than physics.
If strong tail wind, cut the fuel fed to the engines so just enough air speed to not stall

And ground speed so you don't arrive at the destination until there is a gate spot at the airport to accommodate your arrival.
Otherwise you will spend time circling awaiting a gate.

Plus wind speed is not always the same speed at all elevations, and some routes let you fly at different elevations t attempt to find a way out of a strong head or tail wind.

 

[Ponderling]

It is more than physics.
If strong tail wind, cut the fuel fed to the engines so just enough air speed to not stall

And ground speed so you don't arrive at the destination until there is a gate spot at the airport to accommodate your arrival.
Otherwise you will spend time circling awaiting a gate.

Plus wind speed is not always the same speed at all elevations, and some routes let you fly at different elevations t attempt to find a way out of a strong head or tail wind.

The other twist is that head wind gives wings natural lift, so fuel to engines can be used to push plane faster. It is not a linear relationship.

 

[JohnHenry]

Even though I voted more, the problem doesn't state whether the plane's 100mph is air speed or ground speed.

 

[onomatopoeia]

... it flies 100 mph so it takes 2 hours...

I think a plane flying at only 50 miles per hour* would fall out of the sky.

*100 miles per hour into a 50 MPH headwind.

 

[Ceiling Cat]

With a 50 mph headwind, the speed of the plane is reduced to 100 mph - 50 mph = 50 mph. So, it takes 2 hours to complete the first leg of the trip. With a 50 mph tailwind, the speed of the plane is increased to 100 mph + 50 mph = 150 mph. One trip is increased in time because of a head wind, and the other is decreased because of a tail wind. It evens out in the end and is equal in time as compared to a trip without headwind or tail wind.

 

[oral.com]

Without nit picking the “it depends “
Headwind: 100-50 = 50 mph
100/50 = 2 hrs
Tailwind:
100+50= 150 mph
100/150= .666 hrs
.66+2= 2.66 hrs

 

[1kevin]

It will take the same time. Regardless of the wind speed, the pilot will make speed adjustments in order to keep to his schedule.

 

[shack]

Headwind: 100-50 = 50 mph

Do we know for sure that there is 1:1 correlation between the speed of the headwind and the amount of drag on the plane's velocity.

 

[SchlongConery]

Do we know for sure that there is 1:1 correlation between the speed of the headwind and the amount of drag on the plane's velocity.

The airplane only feels/sees/is affected by the mass of air it is travelling in.

Think of a bee flying 5 mph in an empty tractor trailer doing 50 mph.

I know the answer to this but am looking forward to the different ways people think about it. there is a worse airplane speed trick debate but I don't want to crash TERB's server!

 

[oral.com]

Do we know for sure that there is 1:1 correlation between the speed of the headwind and the amount of drag on the plane's velocity.

The question is a high school physics problem .

The reality is far more complex . Wind speed is not constant, and a jet can push its speed faster if it has adequate fuel reserves.
The answer should still be the same though (longer flight time), just not as precise.

 

[shack]

The reality is far more complex . Wind speed is not constant, and a jet can push its speed faster if it has adequate fuel reserves.

But since we are not given any more info, we have to assume that the wind is constant and that the amount of thrust/the amount and rate of fuel provided to the engine is also constant.

 

[escortsxxx]

your reasoning is correct
while he goes 150 one way and 50 the other

But since we are not given any more info, we have to assume that the wind is constant and that the amount of thrust/the amount and rate of fuel provided to the engine is also constant.

way plane spends more time going slow than fast

et’s break this down:

1. No Wind: The plane flies 100 miles at 100 mph, so it takes 1 hour each way. The round trip takes 2 hours.
2. With Wind:
   • On the way there, the plane flies into a 50 mph headwind. This effectively reduces its speed to 50 mph (100 mph - 50 mph). So, the 100-mile trip takes 2 hours (100 miles / 50 mph).
   • On the way back, the plane flies with a 50 mph tailwind. This effectively increases its speed to 150 mph (100 mph + 50 mph). So, the 100-mile trip takes approximately 0.67 hours (100 miles / 150 mph).

So, the round trip with wind takes about 2.67 hours (2 hours + 0.67 hours), which is more time than the round trip without wind.

Therefore, the trip with the headwind and tailwind takes more time than the trip with no wind.

but as said we are assuming this is simplified. No vectors etc.

 

[escortsxxx]

et’s break this down:

1. No Wind: The plane flies 100 miles at 100 mph, so it takes 1 hour each way. The round trip takes 2 hours.
2. With Wind:
   • On the way there, the plane flies into a 50 mph headwind. This effectively reduces its speed to 50 mph (100 mph - 50 mph). So, the 100-mile trip takes 2 hours (100 miles / 50 mph).
   • On the way back, the plane flies with a 50 mph tailwind. This effectively increases its speed to 150 mph (100 mph + 50 mph). So, the 100-mile trip takes approximately 0.67 hours (100 miles / 150 mph).

So, the round trip with wind takes about 2.67 hours (2 hours + 0.67 hours), which is more time than the round trip without wind.

Therefore, the trip with the headwind and tailwind takes more time than the trip with no wind.

but as said we are assuming this is simplified. No vectors etc.

Let’s calculate the time taken for the round trip with a 10-degree wind vector:

1. Component Along the Plane’s Direction: This component will affect the plane’s speed. It can be calculated using the formula wind speed * cos(10 degrees). With a wind speed of 50 mph, this gives us 50 mph * cos(10 degrees) = 49.2 mph.
2. With Wind:
   • Headwind Component: On the way there, the plane flies into a headwind. This effectively reduces its speed to plane speed - headwind component = 100 mph - 49.2 mph = 50.8 mph. So, the 100-mile trip takes 100 miles / 50.8 mph = 1.97 hours.
   • Tailwind Component: On the way back, the plane flies with a tailwind. This effectively increases its speed to plane speed + tailwind component = 100 mph + 49.2 mph = 149.2 mph. So, the 100-mile trip takes 100 miles / 149.2 mph = 0.67 hours.

So, the round trip with wind takes about 1.97 hours + 0.67 hours = 2.64 hours, which is more time than the round trip without wind (2 hours).

 

[SchlongConery]

The clue is in groundspeed vs airspeed and time in the air.

The round trip with winds take longer to cover the same ground than a trip without winds.

The time the plane is affected by the winds is increased in a headwind more than it is reduced by a tailwind.

 

[MrPrezident]

1. If you had the most powerful binoculars in the world, could you see the back of your head?
2. If you invented the perfect solvent, what container would you put it in?

 

[SchlongConery]

1. If you had the most powerful binoculars in the world, could you see the back of your head?

No

2. If you invented the perfect solvent, what container would you put it in?

One made of Unobtainium