Find the bearing and airspeed for a plane to fly 630 miles due north in 3 hours if the wind is blowing from a direction of 318* and is blowing
bearing from where? Oh, you must mean heeding.
Oh, and you need to fill in he wind speed. Say it is w. Then you need a resutant speed of 210 mi/hr due north.
Draw the diagram.
So, if the plane's speed is v, then
v^2 = 120^2 + w^2 - 2*120w cos 138°
Then the heading is nθW where sinθ/w = v/sin138°
To solve this problem, we'll need to break it down into two parts: finding the heading, or bearing, and calculating the required airspeed.
1. Finding the Heading (Bearing):
Since the desired route is due north, the heading of the plane will be 360° (or 0°) since north is the reference point.
2. Finding the Airspeed:
To find the required airspeed, we need to account for the wind. The wind speed and direction are given as "318°."
Since the wind is blowing from 318°, it creates a headwind component that opposes the motion of the plane flying north.
To find the headwind component, we'll use trigonometry. We'll break down the wind into its northward and eastward components using a right-angled triangle:
- Northward Component: sin(318°) * Wind Speed
- Eastward Component: cos(318°) * Wind Speed
However, since the wind is blowing from the south (180° from north), we need to subtract the northward component from the distance of the plane's flight.
Northward Distance = 630 miles - sin(318°) * Wind Speed
Now that we have the northward distance, we can calculate the required airspeed. The formula for airspeed is:
Airspeed = Northward Distance ÷ Time = (630 miles - sin(318°) * Wind Speed) ÷ 3 hours
To find the wind speed, we need another equation. We know that the bearing of the plane is 360°, indicating that the wind's effect on the plane is negligible in an eastward/westward direction since the wind component is perpendicular to the plane's direction.
Therefore, we can say the northward distance is:
Northward Distance = Airspeed × Time = Airspeed × 3 hours
Substituting this value into the original equation for the northward distance:
Airspeed × 3 hours = 630 miles - sin(318°) * Wind Speed
Now we have two equations:
1. Northward Distance = 630 miles - sin(318°) * Wind Speed
2. Airspeed × 3 hours = 630 miles - sin(318°) * Wind Speed
To solve this system of equations, we can substitute the value for Northward Distance from equation 1 into equation 2:
Airspeed × 3 hours = Northward Distance
Airspeed × 3 hours = (630 miles - sin(318°) * Wind Speed)
Now, we can solve for the Airspeed by rearranging the equation:
Airspeed = (630 miles - sin(318°) * Wind Speed) ÷ 3 hours
However, without the specific wind speed, we cannot calculate an exact airspeed. You would need to provide the wind speed or a way to determine it to get an accurate answer.