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A mole runs 10 meters due East, then runs 9 meters due South, then runs 3 meters due North. The mole then burrows 2 meters down a hole. From its original position, what is the magnitude of the mole's displacement?

Respuesta :

Let the directions are defined by vectors as following

East = + x direction

West = - x direction

North = + y direction

South = - y direction

upwards = + z direction

downwards = - z direction

So here we are given that it moves

1). 10 m East

2). 9 m South

3). 3 m North

4). 2 m down

So we can write it as

[tex]d_1 = 10 \hat i[/tex]

[tex]d_2 = 9 (-\hat j)[/tex]

[tex]d_3 = 3 \hat j[/tex]

[tex]d_4 = 2 (-\hat k)[/tex]

Now total displacement will be given as

[tex]d = d_1 + d_2 + d_3 +d_4[/tex]

[tex]d = 10 \hat i - 9 \hat j + 3 \hat j - 2 \hat k[/tex]

[tex]d = 10 \hat i - 6 \hat j - 2 \hat k[/tex]

now the magnitude of the displacement will be

[tex]d = \sqrt{10^2 + 6^2 + 2^2}[/tex]

[tex]d = 11.8 m[/tex]

so the magnitude of displacement will be 11.8 m


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