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In the figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d₁ = 390 m from the station and at angle 0₁ = 45° above the horizon. The airplane is tracked through an angular change 40 = 120° in the vertical east-west plane; its distance is then d₂ = 760 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. W da ΔΘ Airplane Jº, d₂ Radar dish E

In the figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d₁ = 390 m from the station and at angle 0₁ = 45° above the horizon. The airplane is tracked through an angular change 40 = 120° in the vertical east-west plane; its distance is then d₂ = 760 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. W da ΔΘ Airplane Jº, d₂ Radar dish E

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In the figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d₁ = 390 m from the station and at angle 0₁ = 45° above the horizon. The airplane is tracked through an angular change A0 = 120° in the vertical east-west plane; its distance is then d₂ = 760 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. W (a) Number (b) Number 1012.96 IN i ΔΘ Airplane Radar dish Units Units 3 ° (de E
Transcribed Image Text:In the figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d₁ = 390 m from the station and at angle 0₁ = 45° above the horizon. The airplane is tracked through an angular change A0 = 120° in the vertical east-west plane; its distance is then d₂ = 760 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. W (a) Number (b) Number 1012.96 IN i ΔΘ Airplane Radar dish Units Units 3 ° (de E
Expert Solution
Step 1

Given:

At first, the distance between the station and the airplane is, d1=390 m.

At first, the angle between the station and the airplane above the horizon is, θ1=45∘.

The angular change of the airplane is, ∆θ=120∘.

The distance between the station and the airplane after the angular change is, d2=760 m.

To compute:

(a) the magnitude of the airplane's displacement during this period.

(b) the direction of the airplane's displacement during this period.

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