An archiolohist begins a trip by first walking 30km southeast from the campsite. He stops and sets up a temporal camp for the night.On the second day, he walks 60 km in direction 60degrees northeas, at which point he discovers the ancient city of gold.

(a) detaimine the components of the acheologist's desplacement for each day.
(b) detaimine the components of the R in terms of unit vectors.

See previous post.

To determine the components of the archaeologist's displacement for each day, we need to break down the displacements into their horizontal (east-west) and vertical (north-south) components.

(a) Day 1:
The archaeologist walks 30 km southeast. This means his displacement has components of 30 km towards the east and 30 km towards the south. So, the components of the displacement for Day 1 are:

Horizontal component (x-axis): +30 km (towards the east)
Vertical component (y-axis): -30 km (towards the south)

Day 2:
The archaeologist walks 60 km in a direction 60 degrees northeast. We need to find the horizontal and vertical components using trigonometry.

The horizontal component can be calculated using the cosine of the angle:
Horizontal component (x-axis): 60 km * cos(60) = 60 km * 0.5 = 30 km

The vertical component can be calculated using the sine of the angle:
Vertical component (y-axis): 60 km * sin(60) = 60 km * √3/2 ≈ 51.96 km

Therefore, the components of the displacement for Day 2 are:

Horizontal component (x-axis): +30 km (towards the east)
Vertical component (y-axis): +51.96 km (towards the north)

(b) To determine the components of the displacement R in terms of unit vectors, we need to express the individual components in the i and j directions.

The components of the displacement R are obtained by adding the respective components for each day:

Horizontal component (x-axis): (+30 km) + (+30 km) = +60 km
Vertical component (y-axis): (-30 km) + (+51.96 km) = +21.96 km

Using unit vectors, we can write the displacement R as:

R = 60 km * i + 21.96 km * j