A hiker starts at his camp and moves the following distances while exploring his surroundings: 70.0m north, 2.75 x 10^2m east, 130m at an angle 30.0 degrees north of east, and 1.50 x 10^2m south.

a.) find his resultant displacement from camp. (take east as the positive x-direction and north as the positive y-direction)

b.) would changes in the order in which the hiker makes the given displacements alter his final position?

b) the order does not matter. It's simple vector addition, which is commutative.

a) The displacements for each section of the trip are:

(0,70)
(275,0)
(113,65)
(0,-150)
add them up to get (388,-20)

To find the resultant displacement from the camp, we need to calculate the x-component and y-component of displacement separately and then combine them.

a.) Resultant Displacement:
Given distances:
Distance north = 70.0 m (positive y-direction)
Distance east = 2.75 x 10^2 m (positive x-direction)
Distance at an angle 30.0 degrees north of east = 130 m

1. Calculate the x-component of displacement:
x-component = Distance east + (Distance at an angle * cos(angle))
= (2.75 x 10^2 m) + (130 m * cos(30.0 degrees))
= (2.75 x 10^2 m) + (130 m * 0.866) [cos(30 degrees) = 0.866]
≈ 275 m + 112.78 m
≈ 387.78 m (positive x-direction)

2. Calculate the y-component of displacement:
y-component = Distance north + (Distance at an angle * sin(angle))
= 70.0 m + (130 m * sin(30.0 degrees))
= 70.0 m + (130 m * 0.5) [sin(30 degrees) = 0.5]
= 70.0 m + 65 m
= 135.0 m (positive y-direction)

3. Combine the x-component and y-component of displacement to get resultant displacement:
Resultant displacement = √(x-component^2 + y-component^2)
= √((387.78 m)^2 + (135.0 m)^2)
= √(150580.0 + 18225.0)
≈ √168805.0
≈ 410.69 m

Therefore, the hiker's resultant displacement from the camp is approximately 410.69 m.

b.) Changes in the order of displacements would alter the path the hiker takes but would not affect the final position. The resultant displacement will remain the same regardless of the order in which the hiker makes the given displacements.

To find the resultant displacement of the hiker, we need to add all the displacements together.

a) Let's break down the given displacements into their x and y components:

1. The displacement of 70.0m north means a positive y-displacement of 70.0m.
2. The displacement of 2.75 x 10^2m east means a positive x-displacement of 2.75 x 10^2m.
3. The displacement of 130m at an angle 30.0 degrees north of east can be broken down into its x and y components using trigonometry.
The x-component is given by cos(30°) * 130m = 130m * √3/2 ≈ 112.39m (positive).
The y-component is given by sin(30°) * 130m = 130m * 1/2 = 65m (positive).
4. The displacement of 1.50 x 10^2m south means a negative y-displacement of 1.50 x 10^2m.

Now, let's add the x and y components separately:

Total x-component = (2.75 x 10^2m) + (112.39m) = 287.39m
Total y-component = (70.0m) + (65m) - (1.50 x 10^2m) = -35m

The resultant displacement can be found using the Pythagorean theorem:

Resultant displacement = √(Total x-component^2 + Total y-component^2)
= √((287.39m)^2 + (-35m)^2)
≈ √82653.73m^2
≈ 287m (rounded to the nearest meter)

So, the hiker's resultant displacement from the camp is approximately 287 meters.

b) No, the changes in the order in which the hiker makes the given displacements would not alter his final position. The resultant displacement is independent of the order of individual displacements.