Answer:
The total vertical displacement is
Explanation:
Lets say the position of the boat its at the origin of the coordinate system, this is, in vector form:
This simplifies our problem, as the vertical displacement of the diver its:
Now, in this coordinate system, this is the same as:
<u><em>Be careful. This is only valid in this particular coordinate system.</em></u>
Ok, we can return to our problem.
Starting at position
He first descends 8.0 m, this is :
,
as the unit vector ĵ points upwards. Making the substaction:
,
After this, the diver ascends 5.0 m:
,
Then, he continues descending for another 12.0 m:
The, ascends 4.0 m and then descends for 14.0 m, ascends again for 8.0 m and descends again for 11.0 m, all this, will be :
And this is the total vertical displacement.