ohn and Jack are planning to do a physics lab related to vectors. Starting at the door of their physics classroom, they walk 2.0 meters, south. They make a right hand turn and walk 16.0 meters, west. They turn right again and walk 24.0 meters, north. They then turn left and walk 36.0 meters, west. What is the magnitude of their overall displacement?

D=2m[270o] + 16m[180o] + 24m[90o]+36m[180o].

Add the two 180o vectors directly:
D = 2[270o] + 52[180o] + 24[90o]

X = 2*cos270+52*cos180+24*cos90 = -52 m.
Y = 2*sin270+52*sin180+24*sin90 = 22 m.

D^2 = (-52)^2 + 22^2 = 3188
D = 56.5 m.

To find the magnitude of their overall displacement, we need to consider both the magnitude and direction of each individual displacement.

First, let's break down each displacement into its components:

1. The first displacement is 2.0 meters south. Since it is straight south, it has no east-west component and its south component is 2.0 meters.

2. The second displacement is 16.0 meters west. Since it is straight west, it has no north-south component and its west component is 16.0 meters.

3. The third displacement is 24.0 meters north. Since it is straight north, it has no east-west component and its north component is 24.0 meters.

4. The fourth and final displacement is 36.0 meters west. Since it is straight west, it has no north-south component and its west component is 36.0 meters.

To find the overall displacement, we need to add up the east-west and north-south components separately.

The east-west displacement is the sum of the west components: 16.0 meters + 36.0 meters = 52.0 meters west.

The north-south displacement is the sum of the north components minus the south components: 24.0 meters - 2.0 meters = 22.0 meters north.

Now, we can use the Pythagorean theorem to find the magnitude of the overall displacement. The magnitude (D) is given by D = √(East-West^2 + North-South^2).

Substituting the values, we get D = √(52.0^2 + 22.0^2) = √(2704.0 + 484.0) = √3188.0 = 56.42 meters.

Therefore, the magnitude of their overall displacement is approximately 56.42 meters.