Question

You are standing on a street corner with your friend. You then travel 14.0 m due west across the street and into your apartment building. You travel in the elevator 22.0 m upward to your floor, walk 12.0 m north to the door of your apartment, and then walk 6.0 m due east to your balcony that overlooks the street. Your friend is standing where you left her. how far are you from your friend?

Answer 1

The answer is "26.3 m".

Step-by-step explanation:

The positive value from the x-axis is to the direction east side

The negative value from the x-axis is to the direction west side

The positive value from the y-axis is to the direction upwards side

The negative value from the y-axis is to the direction down words side

The positive value from the z-axis is to the direction southside

The negative value from the z-axis is to the direction north side

If the value is i, j, and k are the unit of the given vectors, which can be defined as follows:

`\hat i, \hat -i, \hat j, \hat -j, \hat k, \hat -k`

The displacements values:

`\underset{d_1}{\rightarrow} = -14 \ \hat i\\\\\underset{d_2}{\rightarrow} = 22\ \hat j\\\\\underset{d_3}{\rightarrow} = -12 \ \hat k\\\\\underset{d_4}{\rightarrow} = 6 \ \hat i\\\\`

calculating the final displacement that is
`\underset{d_5}{\rightarrow}`:

`\Rightarrow \underset{d_1}{\rightarrow}+\underset{d_2}{\rightarrow}+\underset{d_3}{\rightarrow}+\underset{d_4}{\rightarrow}+\underset{d_5}{\rightarrow} =0\\\\\Rightarrow \underset{d_5}{\rightarrow} \ \ = -(\underset{d_1}{\rightarrow}+\underset{d_2}{\rightarrow}+\underset{d_3}{\rightarrow}+\underset{d_4}{\rightarrow})`

`=- (-14 \hat i+ 22 \hat j -12 \hat k+ 6 \hat i)\\\\=- (-8 \hat i+ 22 \hat j -12 \hat k)\\\\=8 \hat i- 22 \hat j +12 \hat k\\`

`|\underset{d_5}{\rightarrow}|=√(8^2 +(- 22)^2 +(12)^2 )\\\\`

`= √(64 + 484 +144 )\\\\= √(208 + 484)\\\\= √(692)\\\\= 26.3 \ m`