Question

If you leave your desk, walk 25 meters west down A hall, turn left and head 55 meters south down B hall, turn left again and head 15 meters east down D hall, turn left and head 55 m north up B hall, turn right and head 10 m east down A hall and return to your seat, what is the magnitude of your displacement?

Answer 1

The magnitude of the displacement is 0 meters.

Step-by-step explanation:

To find your displacement, we can break down your movements into vectors and add them together. Let's use a coordinate system where east is the positive x-axis and north is the positive y-axis.

1. From your starting position, you walk 25 meters west. This gives you a displacement vector of -25i.
2. You then turn left and walk 55 meters south down B hall. This gives you a displacement vector of -55j.
3. Next, you turn left again and walk 15 meters east down D hall. This gives you a displacement vector of 15i.
4. You now turn left once more and walk 55 meters north up B hall. This gives you a displacement vector of 55j.
5. Finally, you turn right and walk 10 meters east down A hall, which gives you a displacement vector of 10i.

To find the total displacement, we can add these vectors together: (-25i) + (-55j) + (15i) + (55j) + (10i) = 0i + 0j = 0.

Therefore, the magnitude of your displacement is 0 meters. You have returned to your original position.