An air-traffic controller notices two aircraft on his radar screen. The first is

Question

An air-traffic controller notices two aircraft on his radar screen. The first is at altitude 800 m, horizontal distance 19.2 km, and 25.0 degree south of cast. The second aircraft is at altitude 1100 m, horizontal distance 17.6 km, and 20.0 degree south of cast. Determine their Cartesian coordinates Determine the distance between the two aircraft. The displacement vectors and shown in the figure below both have magnitudes of 1.75 m. The direction of vector is 40.0 degree. Find A^rightarrow + B^rightarrow. Find A^rightarrow - B^rightarrow. Find B^rightarrow - A^rightarrow Find A^rightarrow - 2B^rightarrow. It is possible to shoot an arrow at a speed as high as 127 m/s, If friction is neglected, how high would an arrow launched at this speed rise if shot straight. How long would the arrow be in the air?

Explanation / Answer

x coordinate of first aircraft = 19.2 * cos(25)

x coordinate of first aircraft = 17.4 km

y coordinate of first aircraft = 19.2 * sin(25)

y coordinate of first aircraft = 8.114 km

z coordinate of first aircraft = 0.8 km

x coordinate of second aircraft = 17.6 * cos(20)

x coordinate of second aircraft = 16.538 km

y coordinate of second aircraft = 17.6 * sin(20)

y coordinate of second aircraft = 6.019 km

z coordinate od second aircraft = 1.1 km

a) cartesian coordinate of first aircraft = (17.4, 8.114, 0.8)

a) cartesian coordinate of second aircraft = (16.538, 6.019, 1.1)

distance between two cartesian points = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

distance = sqrt((16.538 - 17.4)^2 + (6.019 - 8.114)^2 + (1.1 - 0.8)^2)

b) distance between two aircraft = 2.285 km

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