Final answer:
To find the magnitude of the resultant vector, we can break down the velocities into their components and use vector addition to calculate the resultant. The magnitude of the resultant vector is 306.6 mph.
Step-by-step explanation:
To find the magnitude of the resultant vector when a plane is flying with its engines pushing it due north at 300 mph and a wind pushing it 20° west of north at 40 mph, we can use the principles of vector addition. We have two vectors: the velocity of the plane (300 mph due north) and the wind velocity (40 mph at 20° west of north).
We'll break down the velocities into their components. The northward velocity of the plane is 300 mph, and the westward component due to the wind is 40 mph × sin(20°) = 13.7 mph. The northward component due to the wind is 40 mph × cos(20°) = 36.5 mph.
Now, we can use these components to find the resultant using the Pythagorean theorem:
Resultant = √((300 + 13.7)² + 36.5²) = 306.6 mph