What vector represents the displacement of a person who walks 15 km at 45 degrees south of east, then 30 km due west?
First find East component of each
15 cos 45 - 30
Now find south component of each
15 sin 45 + 0
so
East = -19.4 or 19.4 West resultant
South = 10.6
tangent of angle south of West (quadrant 3) = 10.6/19.4 = .547
tan^-1 .547 = 28.7 degrees South of West
magnitude = sqrt (19.4^2+10.6^2)
Ah, the great journey of this person! Let's calculate their displacement vector with a dash of humor, shall we?
First, let's break down the journey into two parts:
Part 1: Walking 15 km at 45 degrees south of east:
This sounds like a complicated way of saying they walked diagonally towards the southeast. To represent this, we can break it down into horizontal and vertical components. The horizontal component is 15 km * cos(45°), and the vertical component is 15 km * sin(45°). Combining these, we get the first part of the displacement vector which is approximately 10.6 km east and 10.6 km south.
Part 2: Walking 30 km due west:
Easy peasy! Going directly west means there's no vertical component, so the displacement vector is purely horizontal and equals 30 km west.
Now, let's add these up for the final result, but don't worry, I won't make you do the math! Taking into account both parts, the overall displacement vector of this person is approximately 10.6 km east, 10.6 km south, and 30 km west.
In summary, the displacement vector can be humorously described as: "I went a bit south, then a bit west, and ended up going against the prevailing direction like a rebellious penguin, covering a total of approximately 10.6 km east, 10.6 km south, and 30 km west!"
Let me know if you need any more amusing assistance!
To represent the displacement of a person who walks 15 km at 45 degrees south of east, then 30 km due west, we can break it down into two separate displacements:
1. Displacement from walking 15 km at 45 degrees south of east:
- Start by drawing a reference line in the east direction.
- From the starting point, draw a diagonal line at 45 degrees, going towards the south.
- Measure the length of this line to represent the distance of 15 km.
- Label this vector as V1.
2. Displacement from walking 30 km due west:
- Start from the end point of V1.
- Draw a line directly towards the west direction.
- Measure the length of this line to represent the distance of 30 km.
- Label this vector as V2.
To find the resultant displacement, we need to add the two vectors together:
- Start by drawing the tail of V2 at the head of V1.
- Draw a line from the tail of V1 to the head of V2 to represent the resultant displacement.
- Measure the length of this line to find the magnitude of the displacement.
- Use a protractor to measure the angle between the resultant displacement and the reference line to find the direction.
The resultant vector represents the displacement of the person who walks 15 km at 45 degrees south of east, then 30 km due west.
To answering this question, we need to break down the displacement into its horizontal (east-west) and vertical (north-south) components.
First, let's consider the first part of the displacement, where the person walks 15 km at 45 degrees south of east. To find the horizontal and vertical components, we can use trigonometry.
The horizontal component is determined by the cosine of the angle, while the vertical component is determined by the sine of the angle. Let's calculate these components:
Horizontal component = 15 km * cos(45 degrees)
Vertical component = 15 km * sin(45 degrees)
Using trigonometric identities (√2/2 ≈ 0.707), we can calculate:
Horizontal component = 15 km * 0.707 ≈ 10.61 km
Vertical component = 15 km * 0.707 ≈ 10.61 km
So, the first part of the displacement can be represented as moving approximately 10.61 km eastward and 10.61 km southward.
Now, let's consider the second part of the displacement, where the person walks 30 km due west. Since this motion is entirely in the westward direction, there are no vertical components.
Thus, the second part of the displacement can be represented as moving 30 km westward.
To find the total displacement, we need to add up the horizontal and vertical components of both parts of the displacement:
Horizontal displacement = 10.61 km + (-30 km) (negative sign indicates the opposite direction)
Vertical displacement = 10.61 km
Summing these components:
Horizontal displacement = 10.61 km - 30 km ≈ -19.39 km (rounded to two decimal places)
Vertical displacement = 10.61 km
Therefore, the vector representing the displacement of the person is approximately -19.39 km east and 10.61 km south.