What happens when a small airplane is flying due north at 150km/H and encounters a wind of 80km/H from the east?
The resultant velocity is the vector sum of these two velocities that is 170.07 km/h. Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
|v| = sqrt((150 km/h)² + (80 km/h)²) = sqrt(22500 + 6400) = sqrt(28900) ≈ 170.07 km/h.
The direction of the resultant velocity can be found using trigonometry. The angle between the resultant velocity and the north direction is given by:
θ = tan^(-1)(80/150)
By substituting the values and calculating the angle, we find that the angle is approximately 28.07 degrees.
Therefore, the resultant ground velocity of the airplane is approximately 170.07 km/h in the north-northeast direction.
Understanding Resultant Ground Velocity
Resultant velocity calculation: When a small airplane is flying due north at 150km/H and encounters a wind of 80km/H from the east, the resultant ground velocity can be calculated by finding the vector sum of these two velocities. This results in a magnitude of approximately 170.07 km/h.
Calculating Magnitude of Resultant Velocity
Pythagorean theorem: By using the Pythagorean theorem, we can determine the magnitude of the resultant velocity. Taking the square root of the sum of the squares of the individual velocities gives us the resultant magnitude of 170.07 km/h.
Finding Direction of Resultant Velocity
Trigonometry: To find the direction of the resultant velocity, we use trigonometry to calculate the angle between the resultant velocity and the north direction. By applying the arctangent function to the ratio of the two velocities, we obtain an angle of approximately 28.07 degrees, indicating a north-northeast direction for the airplane's ground velocity.
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