In order to hike around a portion of Lake Allatoona, a tour guide determines that he must take his group 150 m east, 60 m north, then 75 m west. What is the displacement of the tour group from its initial to final position on opposite sides of the lake?

Try drawing it out to get a better visual. Make sure that when you draw the arrows that you make a scale (for example: 1 cm = 10 meters). After drawing it out, draw a line from the origin/starting point and connect it to the end point from the "75 m west" arrow. Then, measure the line you drew and convert it back into meters. Lastly, measure the angle.

batolisis batolisis · Answer 2 · 2021-08-18T13:07:57+02:00

The displacement of the tour group from initial to final position on opposite sides is : approximately ( 96 m, 38.66° east of north )

Given data

150 m to the east ( AC )

60 m to the north ( CD )

75 m to the west ( DE = AB )

attached below is the graphical representation

let A = initial position

E = final position

The displacement vector of the tour = AE

applying Pythagoras theorem

AE = [tex]\sqrt{(CD)^2 + (AB)^2 }[/tex]

= [tex]\sqrt{60^2 + 75^2}[/tex] ≈ 96 m

next : determine the direction of displacement

assuming θ = angle made by AE with base of diagram

∴ tan θ = 60 / 75

tan θ = 0.8

θ = tan⁻¹ (0.8 )

= 38.66° east of north

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