The diagram below indicates three positions to which a woman travels. She starts at position A, travels 3.0 km to the west to point B, then 6.0 km to the north to point C. She then backtracks, and travels 2.0 km to the south to point D.
a) What is the total displacement of the woman from her initial position, A, to her final position, D?
b) What is the total distance traveled by the woman from her initial position, A, to her final position, D?
I will be happy to critique your thinking on this. Remember the definitions of distance (what distance traveled by the feet) and displacement (how far it is from the starting point, and ending point, directly).
Well, this woman seems to have taken quite the detour! Let's see if we can figure out her total displacement and total distance.
a) To find the total displacement, we need to determine the distance between her initial position (A) and her final position (D) in a straight line. Since she traveled 3.0 km to the west (left) and 2.0 km to the south (down), we can treat these distances as vector quantities. Using some Pythagorean theorem magic, we can find the displacement:
Displacement = √((3.0 km)^2 + (2.0 km)^2)
b) To find the total distance traveled by the woman, we simply add up the distances she traveled from point A to point B, from point B to point C, and from point C to point D. Let's add these up:
Distance = 3.0 km + 6.0 km + 2.0 km
Now that we have the equations, let's crunch some numbers and find out how far this woman ended up!
*Calculating intensifies*
a) The total displacement of the woman from position A to position D is approximately 3.61 km (rounded to two decimal places).
b) The total distance traveled by the woman from position A to position D is 11.0 km.
So, this woman took quite a scenic route! She traveled a straight-line distance of 3.61 km, but the total distance she covered was 11.0 km because of the twists and turns along the way.
I hope that clears things up! Let me know if you need any more assistance or some clownish humor to lighten the mood.
To calculate the total displacement of the woman from position A to position D, we need to find the straight-line distance between the two points.
a) We need to consider the directions and magnitudes of each segment traveled:
Segment AB: The woman traveled 3.0 km to the west. This means the displacement for AB is -3.0 km (negative because it is a westward direction).
Segment BC: The woman traveled 6.0 km to the north. This means the displacement for BC is +6.0 km (positive because it is a northward direction).
Segment CD: The woman backtracked and traveled 2.0 km to the south. This means the displacement for CD is -2.0 km (negative because it is a southward direction).
Now, we add up the displacements:
Displacement AD = AB + BC + CD
Displacement AD = (-3.0 km) + (+6.0 km) + (-2.0 km)
Displacement AD = 1.0 km
Therefore, the total displacement of the woman from her initial position A to her final position D is +1.0 km (1.0 km to the north).
b) To calculate the total distance traveled by the woman, we need to add up the distances covered in each segment:
Distance covered AB = 3.0 km
Distance covered BC = 6.0 km
Distance covered CD = 2.0 km
Total distance traveled AD = AB + BC + CD
Total distance traveled AD = 3.0 km + 6.0 km + 2.0 km
Total distance traveled AD = 11.0 km
Therefore, the total distance traveled by the woman from her initial position A to her final position D is 11.0 km.
To find the total displacement of the woman from her initial position, A, to her final position, D, we need to consider the overall change in position regardless of the path taken.
a) The woman starts at position A and travels 3.0 km west to point B. This means she moved 3.0 km to the left (west) from A. We can represent this as a displacement of -3.0 km in the x-direction.
Next, she travels 6.0 km north from point B to point C. This means she moved 6.0 km upwards (north) from B. We can represent this as a displacement of +6.0 km in the y-direction.
Finally, she backtracks and travels 2.0 km south from point C to point D. This means she moved 2.0 km downwards (south) from C. We can represent this as a displacement of -2.0 km in the y-direction.
To find the total displacement, we add up the x (horizontal) and y (vertical) displacements separately. In this case, the x-displacement is -3.0 km and the y-displacement is +6.0 km -2.0 km = +4.0 km.
Therefore, the total displacement from position A to position D is given by the vector (displacement) (-3.0 km, +4.0 km).
b) To find the total distance traveled by the woman from position A to position D, we need to consider the path taken and the distances traveled along that path.
The woman travels 3.0 km west from A to B. Then, she travels 6.0 km north from B to C. Finally, she travels 2.0 km south from C to D.
To calculate the total distance traveled, we sum up the individual distances traveled. In this case, the woman traveled 3.0 km + 6.0 km + 2.0 km = 11.0 km.
Therefore, the total distance traveled by the woman from position A to position D is 11.0 km.