You have recently been promoted and are now a senior pilot with BHS Exprress, providing courteous and timely service to countless cities across the Northeast. In order to arrive in New York City at the scheduled time, you know you must fly at a speed of 380mph on a course of 160 degrees. You check the weather conditions and find that the wind is blowing at 42 mph from 35 degrees East of North. Find the following information: Eastern Component of the Air velocity, southern component of the air velocity, air speed, heading.
convert these headings and speeds to vectors. You want v such that
u+v = w
then just solve for the x- and y- components of v.
could you please elaborate? How to
I put it in u v and w?
the desired velocity is
w = 380mph on a course of 160° = <130,-357>
The wind is
v = 42 mph from 35° = <-34,-24>
and you want
u+v=w
u+<-34,-24>=<130,-357>
so, clearly
v = <164,-333>
Now convert that to speed and heading.
okay I got different answers. Dont you need to do <42cos35, 42in35> and <380cos160,380sin160>? also, how am I supposed to convert that to speed and heading? Arent the answers the eastern and southern components?
okay I realized what I did wrong on that part, but I still don't know how to convert it to speed and heading
wait, I have those answers but -333 as my x and 164 as my y
To find the Eastern Component of the Air Velocity, Southern Component of the Air Velocity, Air Speed, and Heading, we need to break down the given information and use some vector calculations.
1. Eastern Component of the Air Velocity:
The wind velocity is given as 42 mph from 35 degrees East of North. To find the Eastern Component of the Air Velocity, we need to calculate the component of the wind velocity in the eastward direction.
First, we need to convert the direction of the wind from East of North to East of South (clockwise).
- Since the wind is 35 degrees East of North, the angle with respect to the East direction is 90 degrees - 35 degrees = 55 degrees.
The Eastern Component of the Air Velocity can be calculated as follows:
Eastern Component = Wind Velocity * cos(Angle)
Eastern Component = 42 mph * cos(55 degrees)
Eastern Component ≈ 24.25 mph (rounded to two decimal places)
So, the Eastern Component of the Air Velocity is approximately 24.25 mph.
2. Southern Component of the Air Velocity:
The wind velocity is given as 42 mph from 35 degrees East of North. To find the Southern Component of the Air Velocity, we need to calculate the component of the wind velocity in the southward direction.
The Southern Component of the Air Velocity can be calculated as follows:
Southern Component = Wind Velocity * sin(Angle)
Southern Component = 42 mph * sin(55 degrees)
Southern Component ≈ 34.12 mph (rounded to two decimal places)
So, the Southern Component of the Air Velocity is approximately 34.12 mph.
3. Air Speed:
The air speed is the speed of the aircraft relative to the air, without considering the effect of the wind.
Air Speed can be calculated by using the Pythagorean theorem with the Eastern and Southern Components of the Air Velocity.
Air Speed = sqrt(Eastern Component^2 + Southern Component^2)
Air Speed = sqrt((24.25 mph)^2 + (34.12 mph)^2)
Air Speed ≈ 41.64 mph (rounded to two decimal places)
So, the Air Speed is approximately 41.64 mph.
4. Heading:
The heading is the direction in which the aircraft should be pointed to achieve the desired course of 160 degrees, accounting for the effect of wind.
Considering the wind effect, we can use vector addition to find the heading.
Heading = Course + Angle of Wind (with respect to the aircraft's heading)
Angle of Wind = 180 degrees - angle of wind with respect to north (since wind is blowing from East of North)
Angle of Wind = 180 degrees - 35 degrees = 145 degrees
Heading = Course + Angle of Wind
Heading = 160 degrees + 145 degrees
Heading = 305 degrees
So, the Heading is 305 degrees.