Aircraft Speed with Wind: Calculating New Velocity

In summary, the initial speed of the jet airliner is 795 mph to the east, and it moves into a region with a wind speed of 140 mph in a direction 56 degrees north of east. To find the new speed of the aircraft with respect to the ground, a vector diagram should be drawn with the axes assigned as +y for north, -y for south, +x for east, and -x for west. The first vector representing the plane's speed should be drawn starting from the origin and going east, while the second vector representing the wind should be drawn with an angle of 56 degrees from the +x axis. The resulting vector diagram will help determine the new speed of the aircraft.
  • #1
pringless
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A jet airliner moving initially at 795 mph to the east where there is no wind moves into a region where the wind is blowing at 140 mph in a direction 56 degrees north of east. What is the new speed of the aircraft with respect to the ground? Answer in units of mph.

how can i start this off
 
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  • #2
The first step would be to draw a vector diagram. Draw the normal cartesian coordinate system, assign the axes a direction (i.e. +y is north, -y is south, +x is east, -x is south). Since the plane relative to the air is traveling east at 795 mph draw a vector starting from the origin and going east (+x). Now draw the wind as a vector (starting from origin with an angle of 56 degrees from the +x axes). Now you have a vector diagram. That is the first step. Good Luck!
-HBar
 
  • #3

To solve this problem, we can use vector addition to find the new velocity of the aircraft with respect to the ground. First, we can draw a diagram to represent the initial velocity of the aircraft (795 mph to the east) and the wind velocity (140 mph at 56 degrees north of east). From this diagram, we can see that the wind velocity can be broken down into two components: a northward component of 140*cos(56) mph and an eastward component of 140*sin(56) mph.

Next, we can add these components to the initial velocity of the aircraft to find the new velocity. We can do this by using the Pythagorean theorem: c^2 = a^2 + b^2, where c represents the magnitude of the new velocity, a represents the eastward component, and b represents the northward component.

Plugging in the values, we get c^2 = (795 + 140*sin(56))^2 + (140*cos(56))^2. Solving for c, we get c = √((795 + 140*sin(56))^2 + (140*cos(56))^2) = 855.14 mph.

Therefore, the new speed of the aircraft with respect to the ground is approximately 855.14 mph.
 

1. What is aircraft speed with wind?

Aircraft speed with wind refers to the velocity at which an aircraft is moving in relation to the surrounding air when there is wind present. It takes into account both the speed of the aircraft and the speed and direction of the wind.

2. How is aircraft speed with wind calculated?

Aircraft speed with wind can be calculated by adding the speed of the aircraft to the speed of the wind if they are moving in the same direction. If the wind is blowing in the opposite direction, the speed of the wind is subtracted from the speed of the aircraft.

3. Why is it important to calculate aircraft speed with wind?

It is important to calculate aircraft speed with wind because it affects the time and fuel consumption of a flight. Knowing the true velocity of the aircraft allows for more accurate flight planning and can help pilots make necessary adjustments to their flight path.

4. Can aircraft speed with wind change during a flight?

Yes, aircraft speed with wind can change during a flight due to changes in wind speed and direction. This is why it is important for pilots to regularly monitor and adjust their aircraft speed to maintain a safe and efficient flight.

5. How does altitude affect aircraft speed with wind?

Altitude can affect aircraft speed with wind because wind speed and direction can vary at different altitudes. Pilots must take this into account when calculating their aircraft speed with wind to ensure a smooth and safe flight.

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