A girl delivering newspapers travels 1 blocks west, 2 blocks north, then 4 blocks east.
What is the magnitude of her resultant dis- placement?
Answer in units of blocks.
002 (part 2 of 3) 10.0 points
Find the direction (measured from due east, with counterclockwise positive) of her dis- placement.
Answer in units of ◦.
a. Disp. = -1 + 2i + 4 = 3 + 2i = 3.61.
Blocks.
b. Tan A = 2/3 = 0.66667. A = 33.7o = Direction.
Well, it seems like that girl really knows how to take a detour! Let's calculate her resultant displacement step by step.
First, she travels 1 block west, so we can say her displacement in the x-direction is -1 block.
Then, she travels 2 blocks north, so her displacement in the y-direction is +2 blocks.
Finally, she goes 4 blocks east, which gives a displacement in the x-direction of +4 blocks.
Now, let's determine the resultant displacement using the Pythagorean theorem. The magnitude of her resultant displacement is the square root of the sum of the squares of the x and y displacements.
Magnitude = √((-1)^2 + 2^2 + 4^2) = √(1 + 4 + 16) = √21.
So, the magnitude of her resultant displacement is √21 blocks.
Now, onto the direction! We can use trigonometry to find the angle. The direction is the arctan of the y displacement divided by the x displacement.
Direction = arctan(2/4) = arctan(1/2) = 26.565051◦.
So, the direction of her displacement, measured from due east with counterclockwise positive, is approximately 26.6 degrees. Keep going, girl, but maybe next time take a more direct route!
To find the magnitude of the resultant displacement, we can use the Pythagorean theorem.
First, let's calculate the east-west component of the displacement. The girl traveled 1 block west and then 4 blocks east, so the net displacement in the east-west direction is 4 - 1 = 3 blocks east.
Next, let's calculate the north-south component of the displacement. The girl traveled 2 blocks north.
Now, we can use the Pythagorean theorem:
Magnitude of the resultant displacement = √((east-west component)^2 + (north-south component)^2)
= √((3)^2 + (2)^2)
= √(9 + 4)
= √13
≈ 3.61 blocks
To find the direction of the displacement, we can use the tangent function:
Direction = arctan(north-south component / east-west component)
= arctan(2 / 3)
≈ 33.69 degrees
Therefore, the magnitude of her resultant displacement is approximately 3.61 blocks, and the direction is approximately 33.69 degrees measured counterclockwise from due east.
To find the magnitude of the resultant displacement, we can use the Pythagorean theorem.
First, let's break down the girl's journey into its x and y components.
She travels 1 block west, which means her x displacement is -1 (negative because it is in the west direction).
She travels 2 blocks north, which means her y displacement is +2 (positive because it is in the north direction).
Finally, she travels 4 blocks east, which means her x displacement is +4 (positive because it is in the east direction).
To find the resultant displacement, we can add these x and y displacements together.
In the x direction: -1 + 4 = 3
In the y direction: 2
Using the Pythagorean theorem, we can calculate the magnitude of the resultant displacement.
Magnitude = sqrt(x^2 + y^2)
= sqrt(3^2 + 2^2)
= sqrt(9 + 4)
= sqrt(13)
So, the magnitude of her resultant displacement is sqrt(13) blocks.
To find the direction of the displacement (measured from due east, with counterclockwise positive), we can use trigonometry.
The angle can be found using the inverse tangent function:
θ = tan^(-1)(y/x)
In our case, x = 3 and y = 2.
θ = tan^(-1)(2/3)
Using a calculator, we find that θ ≈ 33.69°.
So, the direction of her displacement is approximately 33.69° from due east, counterclockwise.