Airplane's motion relative to the ground involving wind speed

In summary: V_y)_PG = 0 + (V_y)WG= 0 + (-50mph)= -50mphSo the y-component of the plane's speed relative to the ground is -50mph. In summary, the plane is flying east at a speed of 500mph and is 300 miles east of Chicago. With a wind blowing at a speed of 50mph south, the plane's ground speed is unknown. Later, after flying for 0.6 hours, the pilot expects to land in Cleveland, but the plane's location is also unknown. Using the equation for the plane's speed relative to the ground, we can determine that the y-component of the plane's speed is
  • #1
sp3sp2sp
100
4

Homework Statement


Plane is 300miles E of chicago and it leaves flying east at 500mph. Wind is blowing 50mph south.
What is planes ground speed?
Where is plane 0.6 hours later when pilot expects to land in cleveland?

Homework Equations

The Attempt at a Solution


This is how I set it up
I want PG, which is plane speed relative to ground
W = wind, P = plane, G = ground

(V_x)_PG = (V_x)PW + (V_x)WG
(V_y)_PG = (V_y)PW + (V_y)WG

So now I am filling in the values and it doenst look right, so I wanted to check this preliminary step

(V_x)_PG = (V_x)PW + (V_x)WG --> 500mph = (V_x)PW + 0mph
(V_y)_PG = (V_y)PW + (V_y)WG --> 0mph = (V_y)PW + (-50mph)

I think (V_x)PW should also be 500mph and (V_y)PW should = +50mph to make the equations correct, but the 2 equations are not telling me anything I didnt already know from the question stem.

Is this correct so far?
thanks for any help
 
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  • #2
sp3sp2sp said:
(V_y)_PG = (V_y)PW + (V_y)WG --> 0mph = (V_y)PW + (-50mph)
I would take "flying east" as referring to the heading, i.e. direction relative to the wind.
 
  • #3
OK thanks..but y-component of plane's speed relative to the wind, (V_y)_PW would be 0 wouldn't it? Because it travels east there is no movement in y direction, so equation for y should be
(V_y)_PG = (V_y)PW + (V_y)WG
0mph = +50mph + - 50mph

I was hoping to get opinion if I've even set up equation correct because that's what I think a lot of the problem is about.
thanks
 
  • #4
sp3sp2sp said:
(V_y)_PW would be 0
Yes, so why have you again written
sp3sp2sp said:
(V_y)_PG = (V_y)PW + (V_y)WG
0mph = +50mph + - 50mph
?
 
  • #5
Can someone please walk me through this problem? I am getting more and more confused every time I try to work the problem. Thanks in advance
 
  • #6
sp3sp2sp said:
Can someone please walk me through this problem? I am getting more and more confused every time I try to work the problem. Thanks in advance
Fill in the values in your equation
sp3sp2sp said:
(V_y)_PG = (V_y)PW + (V_y)WG
using your new understanding that Vy,PG is unknown and
sp3sp2sp said:
, (V_y)_PW would be 0
 

Related to Airplane's motion relative to the ground involving wind speed

1. How does wind speed affect an airplane's motion relative to the ground?

Wind speed can affect an airplane's motion relative to the ground in several ways. If the wind is blowing in the same direction as the airplane's travel, it can increase the plane's speed and decrease the time it takes to reach its destination. On the other hand, if the wind is blowing in the opposite direction, it can slow down the airplane and increase the travel time. Additionally, wind speed can also affect the airplane's stability and control, making it more difficult for the pilot to maintain a steady course.

2. Will a stronger headwind cause an airplane to take longer to reach its destination?

Yes, a stronger headwind will cause an airplane to take longer to reach its destination. This is because the wind is blowing against the direction of the airplane's travel, making it more difficult for the airplane to move forward. The stronger the headwind, the slower the airplane's speed will be. This means it will take more time for the airplane to cover the same distance compared to flying with no headwind.

3. Can an airplane fly faster than its speed relative to the ground with the assistance of tailwind?

Yes, an airplane can fly faster than its speed relative to the ground with the assistance of tailwind. This is because the tailwind is blowing in the same direction as the airplane's travel, pushing the airplane forward and increasing its speed. However, it is important for pilots to take caution when flying with strong tailwinds, as it can also affect the airplane's stability and control.

4. How do pilots adjust their flight plans in response to changes in wind speed?

Pilots use various techniques and tools to adjust their flight plans in response to changes in wind speed. They may use weather reports and forecasts to anticipate wind patterns and make adjustments to their route accordingly. They can also adjust the airplane's airspeed and altitude to compensate for changes in wind speed. Additionally, pilots may communicate with air traffic control to receive updates on wind conditions and make necessary changes to their flight plan.

5. Can a strong crosswind affect an airplane's takeoff and landing?

Yes, a strong crosswind can significantly affect an airplane's takeoff and landing. Crosswinds, which are winds blowing perpendicular to the direction of the airplane's travel, can create instability and difficulty for the pilot to maintain the desired course. This is why pilots undergo specific training and use techniques, such as crabbing and wing-low method, to safely take off and land in strong crosswinds.

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