Final answer:
The distance between two planes after 1 hour can be calculated by using vector addition and trigonometry to find each plane's displacement components and then applying the Pythagorean theorem. The bearing of the second plane from the first can be determined by taking the inverse tangent of the southward to horizontal distance ratio.
Step-by-step explanation:
The question involves calculating the distance between two planes flying in different directions and the bearing of one plane from another after 1 hour. To solve this problem, we need to apply principles of vector addition and the use of trigonometry to find the components of each displacement.
Since the two planes take off at the same time from the same airport and fly for 1 hour, their distances traveled will be equal to their respective speeds. For the first plane flying S 45.0° E at 235 mph, its eastward and southward components can be found by multiplying the speed by cos(45°) and sin(45°) respectively.
Similarly, for the second plane flying S 45.0° W at 295 mph, its westward and southward components will be the same since the angle is also 45°, but the westward component will be positive, and the eastward negative.
To find the distance between the two planes after one hour, we subtract the eastward component of the second plane from the eastward component of the first plane to get the horizontal distance between them.
Then we combine this with the southward component (since they are the same for both planes) using the Pythagorean theorem to find the total distance. To find the bearing of the second plane from the first after 1 hour, we use inverse tangent (arctan) of the ratio of the southward distance to the horizontal distance to find the angle.