A girl delivering newspapers travels 3 blocks west, 8 blocks north, then 5 blocks east.

1) What is the magnitude of her resultant displacement? Answer in units of blocks.
2) Find the direction (measured from due east, with counterclockwise positive) of her displacement. Answer in units of â—¦.
3) What is the total distance she travels? Answer in units of blocks.
Plz help

Sure! I can help you with that. Let's break down the steps one by one.

1) To find the magnitude of her resultant displacement, we can use the Pythagorean theorem. The west and east displacements cancel each other out, and the north displacement can be represented as the vertical side of a right triangle.

So, using the Pythagorean theorem:
Resultant displacement^2 = (north displacement)^2 + (west displacement + east displacement)^2

Resultant displacement^2 = (8)^2 + (3 + 5)^2
Resultant displacement^2 = 64 + 64
Resultant displacement^2 = 128

Taking the square root of both sides, we get:
Resultant displacement = sqrt(128)
Resultant displacement ≈ 11.31 blocks

Therefore, the magnitude of her resultant displacement is approximately 11.31 blocks.

2) To find the direction of her displacement, we can use trigonometry. We can calculate the angle using the inverse tangent function.

Direction = atan(north displacement / (west displacement + east displacement))
Direction = atan(8 / (3 + 5))
Direction = atan(8 / 8)
Direction = atan(1)

Using a calculator, arctan(1) is approximately 45 degrees.

Therefore, the direction of her displacement is 45 degrees.

3) To find the total distance she travels, we simply need to add up the distances travelled in each direction.
Total distance = north distance + west distance + east distance
Total distance = 8 + 3 + 5
Total distance = 16 blocks

So, the total distance she travels is 16 blocks.

I hope this helps! Let me know if you have any other questions.

Sure, I can help you with that.

1) To find the magnitude of her resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the distance she travels west and east can be considered as the horizontal sides of a right triangle, while the distance she travels north can be considered as the vertical side. So, the magnitude of her resultant displacement can be found using the formula:

Resultant displacement = sqrt((Distance west - Distance east)^2 + (Distance north)^2)

Given that she travels 3 blocks west, 8 blocks north, and then 5 blocks east, we can substitute these values into the formula:

Resultant displacement = sqrt((3 - 5)^2 + 8^2)
Resultant displacement = sqrt((-2)^2 + 64)
Resultant displacement = sqrt(4 + 64)
Resultant displacement = sqrt(68)
Resultant displacement ≈ 8.246 blocks

Therefore, the magnitude of her resultant displacement is approximately 8.246 blocks.

2) To find the direction of her displacement, we can use trigonometry. The direction is typically measured counterclockwise from due east.

First, we need to determine the angle θ between the east direction and the resultant displacement. We can calculate this using the inverse tangent function:

θ = arctan((Distance north) / (Distance east - Distance west))

Substituting the values, we have:

θ = arctan(8 / (5 - 3))
θ = arctan(8 / 2)
θ = arctan(4)
θ ≈ 63.43°

Therefore, the direction of her displacement is approximately 63.43° counterclockwise from due east.

3) To find the total distance she travels, we simply need to add up the distances traveled in each direction.

Total distance = (Distance west) + (Distance north) + (Distance east)
Total distance = 3 + 8 + 5
Total distance = 16 blocks

Therefore, the total distance she travels is 16 blocks.

8 north and 2 east

so
sqrt(64+4)

tan angle north of east = 8/2 = 4

3 + 8 + 5 = 16