Answer:
Total distance traveled is 140 meters.
Total displacement is 63.25 meters in a direction 71.57 degrees north of east.
Step-by-step explanation:
To find your distance and displacement, we'll break down your movements step by step.
You walk 10 meters south (S).
You walk 15 meters east (E).
You walk 30 meters south (S) again.
You walk 35 meters west (W).
You walk 20 meters south (S) once more.
Finally, you walk 30 meters west (W).
Let's calculate:
Distance: Distance is the total length of the path traveled. To find the distance, you sum up all the individual distances traveled in each direction.
Distance = 10m (S) + 15m (E) + 30m (S) + 35m (W) + 20m (S) + 30m (W)
Distance = 10m + 15m + 30m + 35m + 20m + 30m
Distance = 140 meters
So, your total distance traveled is 140 meters.
Displacement: Displacement is the straight-line distance between your starting point and ending point (the shortest distance between two points). To find the displacement, we can use the Pythagorean theorem because your movements form a right-angled triangle.
First, calculate the east-west displacement:
East-West Displacement = 15m (E) - 35m (W)
East-West Displacement = 15m - 35m
East-West Displacement = -20 meters (negative because you ended up to the west of your starting point)
Next, calculate the north-south displacement:
North-South Displacement = 10m (S) + 30m (S) + 20m (S)
North-South Displacement = 10m + 30m + 20m
North-South Displacement = 60 meters
Now, we can use these two displacements to find the total displacement (vector sum):
Displacement = √((East-West Displacement)^2 + (North-South Displacement)^2)
Displacement = √((-20)^2 + (60)^2)
Displacement = √(400 + 3600)
Displacement = √4000
Displacement ≈ 63.25 meters
So, your total displacement is approximately 63.25 meters in a direction approximately 71.57 degrees north of east.