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Answer :
Final answer:
The displacement of each plane is calculated based on its velocity and time, and decomposed into x and y components. The distance between the two planes is determined by subtracting the respective components of their displacements and using the Pythagorean theorem.
Explanation:
The question involves an application of vector addition and trigonometry in physics. The displacement of each plane is given by the product of its speed and time. Since they move in different directions, we cannot simply add or subtract these displacements. Instead, use vector addition to find the result.
First, decompose the displacement of each plane into x (horizontal) and y (vertical) components. For a given velocity v at angle θ, the horizontal and vertical components are v*cos(θ) and v*sin(θ), respectively. In this case, the x and y components of the first plane's displacement after 2 hours will be 750*2*cos(37.6) and 750*2*sin(37.6), respectively. Similarly, for the second plane, they are 590*2*cos(131) and 590*2*sin(131).
Then, subtract the x-components and y-components of the two planes' displacements to get the x and y components of the relative displacement. Finally, use the Pythagorean theorem to find the magnitude of the relative displacement, which represents the distance between the two planes.
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