In what direction should the aircraft head?

In summary, the pilot of an aircraft with a speed of 205 km/h wishes to fly due west in a 50.0 km/h wind blowing toward the south. To determine the direction and speed, the equation c^2 = a^2 + b^2 is used, resulting in a direction of 14.1 degrees north of west and a speed of 1.99 km/h. The pilot must adjust the direction of the plane with a speed of 205 km/h to compensate for the wind and achieve a due west flight.
  • #1
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Homework Statement


The pilot of an aircraft wishes to fly due west in a 50.0 km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 205 km/h.
a.In what direction should the aircraft head?
b. What should its speed be relative to the ground?


Homework Equations


c^2 = a^2 + b^2


The Attempt at a Solution


for the degree, i got 13.7 but the answer is 14.1 north of west
tan^-1 = (50/205) = 13.7
for the speed, I did (-50) ^2 + (-205)^2 = c^2, but that didn't match the answer of 1.99km/h
 
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  • #2
whats your reasoning?
 
  • #3
Well, i put it into a triangle, -50km/h going south, -205km/h west, then found the hypotenuse, which does not match the answer. For the angle, I realize that the angle given in the answer is north west, while mine was south of west, I just don't know where to begin.
 
  • #4
why did you put 205 going west? isn't that the direction you want to find? try 205 at some unknows angle, say [tex] \theta [/tex], and then find what [tex] \theta [/tex] should be if you want the final direction to be west.
 
  • #5
heres a picture that may help you.
 

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  • #6
Wouldn't the 205 be on the X axis because it is without the wind. The speed with the wind would be the hypotenuse I assumed.
 
  • #7
205 km/h is the speed of the plane without wind. not its velocity. now if you add wind, its speed will change, and also its direction, whatever direction it was in. if it was flying directly into the wind, its direction would be the same, i.e opposite to the wind, and its speed would be reduced. you have to choose the direction of the plane with speed 205 km/h such that the direction is changed such that it moves west.
 
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  • #8
You want the "resultant"- the sum of the wind and the airplanes motion- that is to be "due West"- along the x-axis. It is the 205 km/h that is the hypotenuse of the triangle.
 

Related to In what direction should the aircraft head?

1. What factors determine the direction an aircraft should head?

The direction an aircraft should head is determined by a variety of factors, including the aircraft's destination, flight plan, wind conditions, weather patterns, and air traffic control instructions.

2. How does the aircraft's destination affect the direction it should head?

The aircraft's destination is an important factor in determining its direction because it dictates the overall flight path. The aircraft must follow a specific route to reach its destination, which may involve heading in a certain direction or making intermediate turns.

3. Why do wind conditions play a role in determining the direction an aircraft should head?

Wind conditions can significantly impact an aircraft's flight path and must be taken into account when determining the direction it should head. Strong headwinds can slow down the aircraft and require it to head in a different direction to reach its destination on time.

4. How do weather patterns factor into deciding the direction an aircraft should head?

Weather patterns can affect the safety and efficiency of an aircraft's flight. Thunderstorms, high winds, and other severe weather conditions can require the aircraft to change its direction or alter its flight path to avoid dangerous weather.

5. What role do air traffic control instructions play in determining the direction an aircraft should head?

Air traffic control instructions are crucial in determining the direction an aircraft should head. Pilots must follow the instructions given by air traffic control to ensure the safety of all aircraft in the airspace. These instructions may include specific headings or turns to avoid other aircraft or navigate through busy airspace.

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