# Direction of displacement vector

• dlthompson81
In summary, the problem involves determining the length and direction of a displacement vector given a boy's movements in different directions. The length of the displacement vector is 15.3 blocks and the direction is incorrect at 90 degrees due to not drawing the diagram to scale. The correct method is to add the vectors and use trigonometry to determine the angle, which should be rounded off to 1 decimal point.
dlthompson81
I got this problem that states:

A boy runs 11.3 blocks North, 5.6 blocks Northeast, and 4.7 blocks West. Determine the length of the displacement vector that goes from the starting point to his final position.

I got the answer to this part. It was 15.25979798 blocks.

Here is the next part:

Determine the direction of the displacement vector. Use counterclockwise as the positive angular direction, between the limits of -180 degrees and +180 degrees measured from the East. Answer in units of degrees.

Now when I drew this out I got a diagram with the first vector going north at 90 degrees, the second vector goes northeast at 45 degrees, and the third vector goes back west at 45 degrees which is back parallel to the x-axis. From the looks of my diagram the head of the final vector stops when it gets to the point where the first vector would have intersected it had it kept going. I entered 90 degrees, but it told me that was wrong. Where did I go wrong? Thanks for the help.

Do it right. Add the three vectors as vectors and then find the magnitude of the resultant.

You probably didn't draw it to exact scale. I assume you solved for the magnitude of the displacemnt by using sq rt of sum of squares? The angle is determined using what trigonmetric relationship between the y and x components of the resultant displacement? (Please round off your answers to not more than 1 decimal point).

## 1. What is a displacement vector?

A displacement vector is a mathematical representation of the change in position of an object in space. It includes both the magnitude (distance) and direction of the change.

## 2. How is the direction of a displacement vector determined?

The direction of a displacement vector is determined by the angle it forms with a reference axis or direction. This can be calculated using trigonometric functions or by using a protractor on a graph.

## 3. Can a displacement vector have a negative direction?

Yes, a displacement vector can have a negative direction. This indicates that the object has moved in the opposite direction of the reference axis.

## 4. What is the difference between displacement and distance?

Displacement is a vector quantity that represents the change in an object's position. Distance, on the other hand, is a scalar quantity that represents the total length of the path traveled by an object. Displacement takes into account both the magnitude and direction of the change, while distance only considers the total length.

## 5. How is the direction of a displacement vector related to its components?

The direction of a displacement vector is related to its components through trigonometric functions. The x-component represents the horizontal displacement, while the y-component represents the vertical displacement. The direction can be calculated using the inverse tangent function of the y-component divided by the x-component.

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