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Loto begins at his back door and walk 8 yards east, 6 yards north, 12 yards east, and 5 yards north to the barn door. About how many yards less would he walk if he could walk directly from the back door to the barn door?

Respuesta :

facundo3141592

If he could walk directly from the back door to the barn door, he would walk 10.2 yards less.

First, let's define our coordinate axis, I will use north as the y-axis and east as the x-axis.

So let's assume that Loto begins at the point (0, 0).

Then:

  • He moves 8 yards east, to: (8yd, 0)
  • He moves 6 yards north, to: (8yd, 6yd)
  • He moves 12 yards east, to: (20yd, 6yd)
  • He moves 5 yards north, to: (20yd, 11yd)

So he walked a total of 8yd + 6yd + 12yd + 5yd = 33yd

So he just moves from (0, 0) to (20yd, 11yd), thus the displacement is:

[tex]D =\sqrt{(20yd - 0yd)^2 + (11yd - 0yd)^2} = 22.8ft[/tex]

So, if he could walk directly he would only walk 22.8 ft

The difference is:

33yd - 22.8yd = 10.2 yd.

He would walk 10.2 yards less if he could walk directly from the back door to the barn door.

If you want to learn more about displacements, you can read:

https://brainly.com/question/13271165

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