### Video Transcript

A speedboat passes by markers at
the points A, B, and C, as shown in the diagram. Positive displacement is considered
to be away from A, toward C. What is the displacement of the
boat from A when it is at C minus the displacement of the boat from C when it is at
A?

In this question, we’re shown a
diagram of a speedboat and three different position markers. We’re told that positive
displacement is defined to be away from A toward C. In other words, positive
displacement is from right to left across the screen. We need to figure out the
displacement of the boat from point A when it’s at point C minus its displacement
from point C when it’s at A.

Let’s start by figuring out the
boat’s displacement from point A when it’s at point C. We can see from the diagram that
there is a straight-line distance of 250 meters between point C and point A. So, the magnitude of the boat’s
displacement from point A must also be 250 meters. However, since displacement is a
vector quantity, we also need to take direction into account. We already know that positive
displacement is considered towards the left-hand side of the screen. Since point C is to the left of
point A, the displacement of the boat from point A is also in the positive
direction. So, the displacement of the boat
from point A is equal to positive 250 meters.

Now let’s find the boat’s
displacement from point C when it’s at point A. Again, the magnitude of this
displacement must be 250 meters. However, this displacement is now
towards the right-hand side of the screen, which is the opposite direction to
before. This means the boat’s displacement
is now in the negative direction. So, the boat’s displacement is
equal to negative 250 meters.

Now, all we need to do is work out
the difference between the two values we have found. The displacement of the boat from A
when it is at C minus the displacement of the boat from C when it is at A is equal
to positive 250 meters minus negative 250 meters. This is equal to 500 meters.

So, our answer to this question is
that the displacement of the boat from A when it is at C minus the displacement of
the boat from C when it is at A is equal to 500 meters.