I'm having trouble figuring this out. An airplane has an airspeed of 160 mph. It is to make a flight in a direction of 80° while there's a 20 mph wind from 310°. What will the airplane's actual heading be?
I'd appreciate any help especially on how you determined what angles to use. Thank you.
Vr = 160[80o] + 20[310o] = Resultant velocity.
Vr = (160*Cos80+20*Cos310) + (160*sin80+20*sin310)i
Vr = 40.64 + 142.25i = 147.7mph[74.1o]
Heading = 74.1o
To determine the airplane's actual heading, you can use vector addition. Here's how you can approach this problem:
1. Draw a diagram: Start by drawing a diagram that represents the given information. Draw an arrow to represent the airplane's airspeed of 160 mph in the direction of 80°. Then draw another arrow to represent the wind speed of 20 mph in the direction of 310°. Label these arrows accordingly.
2. Find the resultant vector: To find the airplane's actual heading, you need to find the resultant vector of the airplane's airspeed and the wind speed. This can be done by adding the two vectors using the rules of vector addition.
a. Resolve vectors into their components: Convert both vectors into Cartesian coordinate form by resolving them into their x and y components.
- The airplane's airspeed vector can be divided into horizontal (x-axis) and vertical (y-axis) components using trigonometry. The horizontal component can be found by multiplying the airspeed (160 mph) by the cosine of the angle (80°), and the vertical component can be found by multiplying the airspeed by the sine of the angle.
- The wind speed vector can also be divided into horizontal and vertical components in the same way, using the wind speed (20 mph) and the angle (310°).
b. Add the x and y components separately: Add the horizontal components and vertical components separately to find the resultant vector's x and y components.
c. Use the x and y components to find the magnitude and direction: The magnitude of the resultant vector can be found using the Pythagorean theorem: the square root of (x component squared + y component squared). To find the direction, you can use the inverse tangent (arctan) function. The angle you get will be measured clockwise from the positive x-axis.
3. Determine the actual heading: The actual heading of the airplane is the direction the resultant vector is pointing. This heading is measured clockwise from the north, which means you need to convert the angle you obtained in the earlier step into the appropriate reference frame.
Once you've completed these steps, you should be able to determine the airplane's actual heading.