Question

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?

Answer 1

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

$d_1 = 10 \hat i$

$d_2 = 9 (-\hat j)$

$d_3 = 3 \hat j$

$d_4 = 2 (-\hat k)$

Now total displacement will be given as

$d = d_1 + d_2 + d_3 +d_4$

$d = 10 \hat i - 9 \hat j + 3 \hat j - 2 \hat k$

$d = 10 \hat i - 6 \hat j - 2 \hat k$

now the magnitude of the displacement will be

$d = \sqrt{10^2 + 6^2 + 2^2}$

$d = 11.8 m$

so the magnitude of displacement will be 11.8 m