What is the resultant of two displacements?

Answer 1

The shortest distance from start to finish.

Answer 2

If we look at two displacement events, we will see a net displacement as a result. Certainly an object can be moved a certain distance, and then moved back. This will result in a net displacement of zero. But in any case, we might want to use a vector to represent each displacement to find a net displacement. Let's look at something simple and easy to see how that vector thing works. Picture a Chess or checker board in front of you on the table. Just the board. Start in the bottom left corner and plot a displacement vector of three squares to the right. We draw an arrow from the very bottom left corner to the right across the bottom of three squares. The starting point is called the "tail" and the end point with the arrow on it is called the "head" of the vector. Got that one? Now we're going to plot a displacement vector three squares up. Draw an arrow from the bottom left corner three squares up. You have two arrows three squares long. Both start in the same place. Those are your two displacement vectors. Now for the trick part. "Pick up" the second vector. You're going to "move" it and "connect" it to the first vector. And you'll put the "tail" of the second vector on the "head" of the first vector. Now look at what you have. The first vector is as it was, but the second vector is at the arrow (the head) of the first vector and goes up those three squares. You've just done a vector addition. You know what's next - draw a third vector from the bottom left corner to the head of the second vector. This third vector will slant up at a 45 degree angle and go to the head of the second vector. This third vector could be called the displacement vector, as it shows you where you end up if you do the two displacements as asked. Simple and easy. Not all displacement vectors will be this simple, but you can plot any one of them just as easily. That is, you can add any two vectors in just this way. Draw the first one and then start the second one where you ended up with the first one. Then draw your third vector from the point of origin to the end point of that second vector. Presto! Your displacement problem is solved! And it's expressed as that third vector. The length of the third vector is the magnitude of the net displacement. With the application of trigonometric functions to each vector, you can find out exactly where you end up, and how far (the displacement) from the point of origin you finish your journey. Very similar to graphing two line segments, which is effectively what you are doing. If you are concerned with the energy expended in this activity, a similar process will allow you to make the calculations necessary to find your answer.

Answer 3

If we look at two displacement events, we will see a net displacement as a result. Certainly an object can be moved a certain distance, and then moved back. This will result in a net displacement of zero. But in any case, we might want to use a vector to represent each displacement to find a net displacement. Let's look at something simple and easy to see how that vector thing works.

Picture a chess or checker board in front of you on the table. Just the board. Start in the bottom left corner and plot a displacement vector of three squares to the right. We draw an arrow from the very bottom left corner to the right across the bottom of three squares. The starting point is called the "tail" and the end point with the arrow on it is called the "head" of the vector. Got that one? Now we're going to plot a displacement vector three squares up. Draw an arrow from the bottom left corner three squares up. You have two arrows three squares long. Both start in the same place. Those are your two displacement vectors. Now for the trick part.

"Pick up" the second vector. You're going to "move" it and "connect" it to the first vector. And you'll put the "tail" of the second vector on the "head" of the first vector. Now look at what you have. The first vector is as it was, but the second vector is at the arrow (the head) of the first vector and goes up those three squares. You've just done a vector addition. You know what's next - draw a third vector from the bottom left corner to the head of the second vector. This third vector will slant up at a 45 degree angle and go to the head of the second vector. This third vector could be called the displacement vector, as it shows you where you end up if you do the two displacements as asked. Simple and easy.

Not all displacement vectors will be this simple, but you can plot any one of them just as easily. That is, you can add any two vectors in just this way. Draw the first one and then start the second one where you ended up with the first one. Then draw your third vector from the point of origin to the end point of that second vector. Presto! Your displacement problem is solved! And it's expressed as that third vector. The length of the third vector is the magnitude of the net displacement. With the application of trigonometric functions to each vector, you can find out exactly where you end up, and how far (the displacement) from the point of origin you finish your journey. Very similar to graphing two line segments, which is effectively what you are doing.

If you are concerned with the energy expended in this activity, a similar process will allow you to make the calculations necessary to find your answer.

Jang Woona Yeun