A woman starts at point A and travels 3.0 km to the west to point B then 6.0 into the north to point C. She then backtracks and travels 2.0km to the south to point D. What is the woman’s total displacement?
-3.0, 6.0,-2.0
s=SF-SI
-3.0,6.0,-2.0-0.0(initial)
Answer= -7 ??? is this correct??
To find the total displacement of the woman, you need to calculate the vector sum of her individual displacements. Displacement is a vector quantity, which means it has both magnitude (distance) and direction.
In this case, the woman travels 3.0 km west (point A to point B) and then 6.0 km north (point B to point C), which gives you two displacement vectors: -3.0 km (west) and +6.0 km (north).
To calculate the vector sum, you need to add the magnitudes in the respective directions. Since we're dealing with a two-dimensional problem, you need to break down the vectors into their horizontal (x) and vertical (y) components.
-3.0 km west can be written as (-3.0, 0.0) in vector notation, where -3.0 represents the magnitude in the x-direction (west) and 0.0 represents the magnitude in the y-direction (north/south).
6.0 km north can be written as (0.0, 6.0) in vector notation, where 0.0 represents the magnitude in the x-direction (west/east) and 6.0 represents the magnitude in the y-direction (north).
Now, add the corresponding components to get the resultant displacement vector:
(-3.0, 0.0) + (0.0, 6.0) = (-3.0 + 0.0, 0.0 + 6.0) = (-3.0, 6.0)
So, the woman's total displacement is (-3.0, 6.0), which means she ended up 3.0 km west and 6.0 km north from her starting point.
Therefore, the answer is not -7.0 km; it is (-3.0, 6.0) km.