An ice skater skates 28 m southwest, then

56 m east, and finally 84 m in a direction
50.3
◦ north of east.Find the magnitude of the displacement required to bring the skater back to her starting
point.
Answer in units of m

To find the magnitude of the displacement required to bring the skater back to her starting point, we need to calculate the total displacement.

Step 1: Break down the displacements into their x and y components.

The first displacement is 28 m southwest, which can be broken down into x and y components:
x1 = -28 * cos(45°)
y1 = -28 * sin(45°)

The second displacement is 56 m east, which only has an x component:
x2 = 56

The third displacement is 84 m in a direction 50.3° north of east, which can be broken down into x and y components:
x3 = 84 * cos(50.3°)
y3 = 84 * sin(50.3°)

Step 2: Calculate the total displacement.

The total x and y components can be calculated by summing up the individual components:
x_total = x1 + x2 + x3
y_total = y1 + y3

Step 3: Calculate the magnitude of the displacement.

The magnitude of the displacement (d) can be found using the Pythagorean theorem:
d = sqrt(x_total^2 + y_total^2)

Plugging in the values and calculating:
d = sqrt((-28 * cos(45°) + 56 + 84 * cos(50.3°))^2 + (-28 * sin(45°) + 84 * sin(50.3°))^2)

After evaluating this equation, the magnitude of the displacement required to bring the skater back to her starting point will be in units of meters.

To find the magnitude of the displacement required to bring the skater back to her starting point, we need to calculate the net displacement.

First, let's break down the skater's movement into the components of motion: east (+x) and north (+y). Let's assume the starting point is the origin (0,0).

1. The skater skates 28 m southwest. This means she moves 28 m in the southwest direction, which is down and to the left (-x and -y). So, the displacement can be represented as (-28, -28).

2. Next, the skater skates 56 m east. This adds to the east component of the displacement, so the displacement becomes (-28+56, -28) = (28, -28).

3. Finally, the skater skates 84 m in a direction 50.3° north of east. To find the components, we can use trigonometry.

The north component can be calculated using sin(50.3°) = y/84. Rearranging the equation, we get y = 84 * sin(50.3°) = 63.58 m (rounded to two decimal places).

The east component can be calculated using cos(50.3°) = x/84. Rearranging the equation, we get x = 84 * cos(50.3°) = 64.44 m (rounded to two decimal places).

Adding the north and east components to the displacement gives (28 + 64.44, -28 + 63.58) = (92.44, 35.58).

Now, we can find the magnitude of the displacement using the Pythagorean theorem:
Magnitude = sqrt[(92.44)^2 + (35.58)^2] ≈ 99.04 m

Therefore, the magnitude of the displacement required to bring the skater back to her starting point is approximately 99.04 m.

28 @ S45W = (-19.8,-19.8)

56 @ E = (50,0)
84 @ E53N = (50.5,67.1)

Add them up to get (80.7,47.3)

So, we need (-80.7,-47.3) to get back to (0,0), a displacement of 93.5 m