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Question Video: Determining the Displacements between Positions Physics • 9th Grade

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?

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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.

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