Answer :
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Final answer:
The girl's resultant displacement is 6.32 blocks at an angle of 73.74 degrees north of east. The total distance she travels is 16.00 blocks.
Explanation:
To find the resultant displacement, we need to calculate the net displacement by considering the individual displacements in each direction. The girl travels 4.00 blocks west, 6.00 blocks north, and then 6.00 blocks east.
Let's break down the displacements:
- 4.00 blocks west: This displacement is in the negative x-direction.
- 6.00 blocks north: This displacement is in the positive y-direction.
- 6.00 blocks east: This displacement is in the positive x-direction.
To find the resultant displacement, we can add the displacements in the x-direction and the y-direction separately.
In the x-direction, the net displacement is 6.00 blocks east - 4.00 blocks west = 2.00 blocks east.
In the y-direction, the net displacement is 6.00 blocks north.
Using the Pythagorean theorem, we can find the magnitude of the resultant displacement:
Resultant displacement = sqrt((2.00 blocks)^2 + (6.00 blocks)^2) = sqrt(4.00 blocks^2 + 36.00 blocks^2) = sqrt(40.00 blocks^2) = 6.32 blocks.
Therefore, the girl's resultant displacement is 6.32 blocks at an angle of tan^(-1)(6.00 blocks/2.00 blocks) = 73.74 degrees north of east.
To find the total distance traveled, we can simply add up the magnitudes of the individual displacements:
Total distance traveled = 4.00 blocks + 6.00 blocks + 6.00 blocks = 16.00 blocks.
Learn more about resultant displacement and total distance traveled here:
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