Kim an entrepreneur students walks 20m,30°NE,then turns N 30m,and takes 40m W and finally 20m 45°SE to reach the building for his next class.what is kims total displacement

D=20[30o] + 30[90o] + 40[180o]+20[315o]

X=20*Cos30+30*Cos90+40*Cos180+20*Cos315 =

Y=20*sin30+30*sin90+40*sin180+20*sin315
=

Tan A = Y/X. A = ?.

D = X/Cos A, or Y/sin A.

To find Kim's total displacement, we need to calculate the net displacement in terms of magnitude and direction.

Step 1: Convert the given distances and angles to their respective components.

First, we need to break down the given distances and angles into their respective north-south and east-west components.

Given information:
1. Walks 20m.
2. Walks 30° NE.
3. Turns north and walks 30m.
4. Takes 40m west.
5. Finally, walks 20m on a 45° SE direction.

Step 2: Calculate the components of each step.

1. Initial Walk: 20m
The north-south component is 20 * cos(0°) = 20 * 1 = 20 meters.
The east-west component is 20 * sin(0°) = 20 * 0 = 0 meters.

2. Walks 30° NE:
The north-south component is 30 * cos(45°) = 30 * 0.7071 ≈ 21.2132 meters.
The east-west component is 30 * sin(45°) = 30 * 0.7071 ≈ 21.2132 meters.

3. Walks north 30m:
The north-south component is 30 meters, and there is no east-west component.

4. Takes 40m west:
The north-south component is 0 meters, and the east-west component is -40 meters (as it's westward).

5. Walks 20m 45° SE:
The north-south component is -20 * cos(45°) = -20 * 0.7071 ≈ -14.1421 meters.
The east-west component is -20 * sin(45°) = -20 * 0.7071 ≈ -14.1421 meters.

Step 3: Calculate the total north-south and east-west components.

North-south component:
20 + 21.2132 + 30 + 0 - 14.1421 = 57.0711 meters
East-west component:
0 + 21.2132 + 0 - 40 - 14.1421 ≈ -33.929 meters

Step 4: Calculate the magnitude and direction of the total displacement.

Magnitude of the total displacement = √(north-south component^2 + east-west component^2)
= √(57.0711^2 + (-33.929)^2)
≈ √(3250 + 1150.656)
≈ √4400.656
≈ 66.320 meters (rounded to three decimal places)

Direction of the total displacement = tan^(-1)(east-west component / north-south component)
= tan^(-1)(-33.929 / 57.0711)
≈ -30.655°

Therefore, Kim's total displacement is approximately 66.320 meters at an angle of -30.655°.