In the figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d1 = 320 m from the station and at angle θ1 = 31° above the horizon. The airplane is tracked through an angular change Δθ = 124° in the vertical east-west plane; its distance is then d2 = 800 m. Find the (a) magnitude and (b) direction of the airplane's displacement during this period. Give the direction as an angle relative to due west, with a positive angle being above the horizon and a negative angle being below the horizon.

Question

Camille Beasley

Physics

2 December, 17:29

In the figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d1 = 320 m from the station and at angle θ1 = 31° above the horizon. The airplane is tracked through an angular change Δθ = 124° in the vertical east-west plane; its distance is then d2 = 800 m. Find the (a) magnitude and (b) direction of the airplane's displacement during this period. Give the direction as an angle relative to due west, with a positive angle being above the horizon and a negative angle being below the horizon.

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Answers (1)

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Kieran Kaufman · Answer 1

The magnitude and the direction of the displacement is solved by the polar equation

800 ∠ 124° - 320 ∠ 31°

A capable calculator can solved this immediately.

Manually, the x and y components need to be solved using trigonometry. Then, by the Pythagorean theorem, the magnitude is solved. The direction is determined using the x and y components and the tangent function.