3. You travel from New Orleans, Louisiana, with the following vectors:

• New Orleans à Point A: q = 180°, Δd = 483 km
• Point A à Point B: q = 106°, Δd = 347 km
• Point B à Point C: q = 106°, Δd = 347 km
Remember: east = 0°, north = 90°, west = 180
Use the map to find your final destination. Where is the final destination, and what is its displacement from New Orleans? Show a data table containing each vector and its x and y components. Include the values of Δdnetx, Δdnety, Δdnet, tan qr, and qr.

d = 483[180o ] + 347[106o] + 347[106o]

d = 483[180 + 694[106o]

X = 483*cos180 + 694*cos106 = -674.3 km
Y = 483*sin180 + 694*sin106 = 667.1 km

tan Ar = Y/X = 667.1/-674.3 = -0.98935
Ar = -44.69o = Reference angle.

A = 180-44.69 = 135.3o

d = X/cosA = -674.3/cos135.3 = 948.7 km
[135.3] = Final destination.

Disp. = 948.7[135.3o] - 483[180o]
X=948.7*cos135.3 - 483*cos180=-191.3 km
Y=948.7*sin135.3 - 483*sin180 = 667.3 km

tan Ar = Y/X = 667.3/-191.3 = -3.48829
Ar = -74o = Reference angle.
A = -74 + 180 = 106o

Disp. = Y/sinA = 667.3/sin106 = 694.2km[106o].

i don't get it

Ah, traveling with vectors, huh? That sounds like a fun adventure! Let's find your final destination and calculate your displacement from New Orleans. Here's a data table to help us out:

Vector | Δdx | Δdy | Δd | tan qr | qr
--------------------------------------------------------
New Orleans à Point A | ? | ? | 483 km | ? | 180°
Point A à Point B | ? | ? | 347 km | ? | 106°
Point B à Point C | ? | ? | 347 km | ? | 106°

To calculate the x and y components, we can use the formulas Δdx = Δd * cos(q) and Δdy = Δd * sin(q). Let's do some math:

1. New Orleans à Point A:
Δdx = 483 km * cos(180°) = -483 km
Δdy = 483 km * sin(180°) = 0 km

2. Point A à Point B:
Δdx = 347 km * cos(106°) = -157.74 km
Δdy = 347 km * sin(106°) = 324.15 km

3. Point B à Point C:
Δdx = 347 km * cos(106°) = -157.74 km
Δdy = 347 km * sin(106°) = 324.15 km

Now, let's find the net displacement values:

Δdnetx = (-483 km) + (-157.74 km) + (-157.74 km) = -798.48 km
Δdnety = 0 km + 324.15 km + 324.15 km = 648.3 km
Δdnet = √((-798.48 km)² + (648.3 km)²) ≈ 1021.31 km

To find tan qr, we can use qr = atan(Δdy/Δdx):

tan qr = tan(atan(Δdnety/Δdnetx)) = tan(atan(648.3 km/-798.48 km)) ≈ tan(-0.694) ≈ -0.805

Now, let's find qr:

qr = atan(Δdnety/Δdnetx) = atan(648.3 km/-798.48 km) ≈ atan(-0.813) ≈ -38.25°

Ta-da! Your final destination is at Point C, and its displacement from New Orleans is approximately 1021.31 km. Just follow the vectors and enjoy your journey!

To find the final destination and its displacement from New Orleans, we can break down each vector into its x and y components, and then sum up these components.

Let's start by creating a data table to record the vectors and their components:

Vector | q (degrees) | Δd (km) | Δdx | Δdy
-------|-------------|---------|-----|-----
NO à A | 180° | 483 km | ΔNOAx | ΔNOAy
A à B | 106° | 347 km | ΔABx | ΔABy
B à C | 106° | 347 km | ΔBCx | ΔBCy

Now, let's calculate the x and y components for each vector:

1. NO à A:
- ΔdNOAx = - Δd * sin(q) [negative because it's west]
- ΔdNOAy = Δd * cos(q) [positive because it's north]

2. A à B:
- ΔdABx = Δd * cos(q)
- ΔdABy = Δd * sin(q)

3. B à C:
- ΔdBCx = Δd * cos(q)
- ΔdBCy = Δd * sin(q)

Let's calculate these components:

Vector | q (degrees) | Δd (km) | Δdx | Δdy
-------|-------------|---------|-----|-----
NO à A | 180° | 483 km | -483 km | 0 km
A à B | 106° | 347 km | 156.8 km | 321.6 km
B à C | 106° | 347 km | 156.8 km | 321.6 km

Now, we can sum up the x and y components to get the total displacement:

Δdnetx = ΔdNOAx + ΔdABx + ΔdBCx
Δdnety = ΔdNOAy + ΔdABy + ΔdBCy

Let's calculate Δdnetx and Δdnety:

Δdnetx = -483 km + 156.8 km + 156.8 km = -169.4 km
Δdnety = 0 km + 321.6 km + 321.6 km = 643.2 km

The displacement from New Orleans can be found using the Pythagorean theorem:

Δdnet = √(Δdnetx² + Δdnety²)

Let's calculate Δdnet:

Δdnet = √((-169.4 km)² + (643.2 km)²) = √(28716.36 km² + 414275.84 km²) ≈ 644.1 km

Therefore, the final destination is approximately 644.1 km away from New Orleans, in the north-northeast direction.