An airplane is flying NW with a ground speed of 600 Km/h. If a 125 Km/h wind from the W suddenly hits the airplane, find the airplane's new speed and direction relative to the ground.
To find the airplane's new speed and direction relative to the ground, we can use vector addition.
Step 1: Draw a diagram illustrating the given information.
- Draw a vector representing the airplane's initial speed and direction. Label it as "Airplane's speed (600 Km/h)" and draw an arrow towards the NW direction.
- Draw a vector representing the wind's speed and direction. Label it as "Wind's speed (125 Km/h)" and draw an arrow towards the W direction.
Step 2: Add the two vectors to find the resultant vector.
- Place the tail of the wind vector at the head of the airplane vector.
- Draw a line connecting the tail of the airplane vector to the head of the wind vector.
- The resultant vector represents the airplane's new speed and direction relative to the ground.
Step 3: Measure the magnitude and direction of the resultant vector.
- Measure the length of the resultant vector. This gives the magnitude of the airplane's new speed relative to the ground.
- Measure the angle between the direction of the resultant vector and the original heading of the airplane. This gives the direction of the airplane's new direction relative to the ground.
In this case, since the airplane is flying NW (northwest) and the wind is coming from the west, the new direction relative to the ground will be affected by both the airplane's initial heading and the wind's direction.
By using vector addition, the magnitude of the resultant vector can be calculated as follows:
Magnitude of the resultant vector = √(600² + 125²) = √(360000 + 15625) = √375625 ≈ 613.11 Km/h
The direction of the resultant vector can be calculated as follows:
tan(θ) = (125/600)
θ = arctan(125/600) ≈ 11.09 degrees
Therefore, the airplane's new speed relative to the ground is approximately 613.11 Km/h, and its new direction relative to the ground is approximately 11.09 degrees north of the original heading.