An airplane’s velocity with respect to the air is 630 mph, and its heading is 𝑁 30° 𝐸. The wind, at the altitude of the plane, is directly from the southeast at 45° and has a velocity of 45 mph. Draw a figure that gives a visual representation of the situation. What is the true direction of the plane, and what is its speed with respect to the ground?
just convert the vectors to x-y components, add them, and you have the resultant.
Can you get that far? If not, where do you get stuck?
I did get to that part, I drew the picture, but I think I kept using the wrong angles, I'm not really sure
630 @ 𝑁 30° 𝐸 = <315.00,545.58>
wind from the SE is in the direction NW, so 45 @ NW = <-31.82,31.82>
Now, if the plane's ground speed is <x,y> we have
<x,y> + <-31.82,31.82> = <315.00,545.58>
x = 346.82
y = 513.76
That translates into a speed of 619.87 in the direction (from the x-axis) of 55.98°. That makes a heading of 145.98°
sorry; the heading is 34.02°
(It's 90-A), not 90+A
To get a visual representation of the situation, let's draw a diagram using the given information.
1. Start by drawing a line to represent the ground and label it as 'Ground' or 'Earth'.
2. Draw an arrow pointing to the northeast (𝑁𝑒) on the ground line. This arrow represents the true direction of the plane.
3. Label the arrow as 'Plane's True Direction'.
4. Draw another arrow starting from the tip of the 'Plane's True Direction' arrow and extending 630 miles per hour to the right. This arrow represents the velocity of the plane with respect to the air.
5. Label this arrow as 'Plane's Air Velocity = 630 mph'.
6. Now, draw another arrow starting from the tip of the 'Plane's Air Velocity' arrow and pointing towards the southeast (𝑆𝐸).
7. The length of this arrow represents the velocity of the wind, which is 45 mph.
8. Label this arrow as 'Wind Velocity = 45 mph'.
9. Finally, draw a line starting from the tail of the 'Plane's True Direction' arrow and extend it so that it intersects with the tail of the 'Wind Velocity' arrow.
10. The line you just drew represents the ground velocity of the plane, which is the result of combining the plane's air velocity and the wind velocity.
Now, let's calculate the true direction of the plane and its speed with respect to the ground.
To find the true direction of the plane, we need to add the directions of the plane's true direction and the wind velocity vectors. This can be done using vector addition.
1. Draw a dashed line, starting from the tail of the 'Plane's True Direction' arrow, parallel to the 'Wind Velocity' arrow.
2. Measure the angle between the dashed line and the 'Ground' line. This angle represents the true direction of the plane.
The measured angle should be approximately 15° north of east.
To find the speed of the plane with respect to the ground, we can use the concept of the Pythagorean theorem.
1. Measure the length of the dashed line that represents the ground velocity of the plane.
2. This length represents the speed of the plane with respect to the ground.
The measured length should give the speed of the plane with respect to the ground.
Now, you have the true direction of the plane and its speed with respect to the ground.