6m due south,10m due east and 5m due north. Find the distance traveled and the displacement of the vector
(0,-6)+(10,0)+(0,5) = (10,-1)
I assume you can find vector lengths.
The distance, naturally, is just 6+10+5
A woman walks 2km due East and then 2km due south. Calculate the displacement of the woman.
To find the distance traveled, we need to add up the lengths of the individual displacements.
Distance traveled = Length of first displacement + Length of second displacement + Length of third displacement
First displacement: 6m due south
Length = 6m
Second displacement: 10m due east
Length = 10m
Third displacement: 5m due north
Length = 5m
Distance traveled = 6m + 10m + 5m = 21m
To find the displacement of the vector, we need to find the net displacement from the starting point to the end point.
Start by representing each displacement as a vector and adding them up.
First displacement: 6m due south
Vector = -6m (south is considered negative in the y-direction)
Second displacement: 10m due east
Vector = +10m (east is considered positive in the x-direction)
Third displacement: 5m due north
Vector = +5m (north is considered positive in the y-direction)
Adding up the vectors, we get:
Net displacement = -6m (south) + 10m (east) + 5m (north)
Since we moved in opposite directions along the y-axis, the north and south components cancel out.
Net displacement = -6m (south) + 10m (east) = -6m + 10m = 4m
So, the distance traveled is 21m and the displacement of the vector is 4m.
To find the distance traveled, you need to calculate the sum of the magnitudes of each individual displacement.
First, let's break down the problem step by step:
1. Start at point A.
2. Move 6m due south, ending at point B.
3. From point B, move 10m due east, ending at point C.
4. Finally, from point C, move 5m due north, ending at the final point D.
Now, let's calculate the distance traveled:
Distance traveled = (distance from A to B) + (distance from B to C) + (distance from C to D)
The distance from A to B is 6m.
The distance from B to C is 10m.
The distance from C to D is 5m.
So the distance traveled is 6m + 10m + 5m = 21m.
Now, let's calculate the displacement. Displacement is a vector quantity that indicates the shortest straight-line distance between the initial and final positions.
To find the displacement, we need to find the magnitude and direction of the resultant vector from point A to point D.
For that, we will need to draw a diagram to visualize the scenario:
A____________B
\ /
\ /
\ /
C__D
From the diagram, we can see that the final point D is 5m north of the starting point A.
Therefore, the displacement is 5m due north.
In summary, the distance traveled is 21m, and the displacement is 5m due north.