How Do You Calculate Vector Displacement from a Plane to a Ship?

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To calculate the vector displacement from the rescue plane to the sinking ship, first represent their positions using the radar station as the origin. The ship's position is given as Vship with coordinates derived from its range of 18.2 km at a bearing of 134°, while the plane's position is Vplane at a range of 20.0 km and bearing of 151°, with an elevation of 2.33 km. The coordinates for both vectors can be calculated using trigonometric functions based on the specified angles. The vector displacement is then found by subtracting the plane's vector from the ship's vector, expressed as Vd = Vship - Vplane. This method provides the necessary vector displacement in the form of i, j, and k components.
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can some1 help me with this question??

A radar station locates a sinking ship at range 18.2 km and bearing 134° clockwise from north. From the same station a rescue plane is at horizontal range 20.0 km, 151° clockwise from north, with elevation 2.33 km. What is the vector displacement from plane to ship, letting i represent east, j north, and k up. Enter answers in this order and include units.

i tried it myself but i can't get the answer. please help
 
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hello yj-k91 and welcome to PF :smile:
consider the radar station as the original point [zero point], then represent the position of both ship and plane in the form of:

Vship=x1i+y1j+z1k

Vplane=x2i+y2j+z2k

now, x and y values can be calculated using the given angles and distances [note that the angles are clockwise from the y-axis], the vector displacement from plane to ship will be:

Vd=Vship-Vplane
 


thank you so much drizzle.
 
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