Final answer:
The angle of the resultant vector is approximately 56.31 degrees when a plane is flying 60 m/s south and drifting southwest at 90 m/s.
Step-by-step explanation:
To find the angle of the resultant vector, we need to use vector addition. Since the plane is flying south at 60 m/s and drifting southwest at 90 m/s, these two velocities can be represented as vectors. The resultant vector is the sum of these two vectors. Using the Pythagorean theorem and trigonometric functions, we can calculate the magnitude and angle of the resultant vector.
Let's represent the southward velocity as vector S and the southwest drift velocity as vector D. The resultant vector R is obtained by adding vectors S and D. Using the Pythagorean theorem, we have R^2 = S^2 + D^2. Substituting the given values, we get:
R^2 = (60 m/s)^2 + (90 m/s)^2 = 3600 m^2/s^2 + 8100 m^2/s^2 = 11700 m^2/s^2
The magnitude of the resultant vector is R = sqrt(11700 m^2/s^2) = 108.11 m/s.
To find the angle of the resultant vector, we can use trigonometric functions. Let's call the angle between the resultant vector R and the south direction angle A. We can use the tangent function to find A:
tan(A) = D/S = 90 m/s / 60 m/s = 1.5
A = arctan(1.5)
A = 56.31 degrees
Therefore, the angle of the resultant vector is approximately 56.31 degrees.