Net Displacement

Displacement is the straight-line distance from the starting point to the final position, regardless of the path taken. If a person walks 3 km North and then 4 km East, the total distance walked is 7 km but the displacement (shortest distance back to start) is 5 km, because the North and East moves form a right-angled triangle (3-4-5 Pythagorean triple). Displacement questions always ask "How far is the person from the starting point?" not "How far did they walk?"

1. Draw the starting point on paper.
2. Plot each move as an arrow: North = up, South = down, East = right, West = left.
3. Cancel out opposite directions: 5 km North then 3 km South = net 2 km North.
4. After cancellation, if the remaining moves are in perpendicular directions (one N/S and one E/W), use Pythagoras: displacement = square root of (a squared + b squared).
5. State the answer with the direction: "5 km, North-East of the starting point."

Example 1: A man walks 6 km North, then 8 km East. How far is he from the start?

• North-South net: 6 km North. East-West net: 8 km East. These are perpendicular.
• Displacement = square root of (6 x 6 + 8 x 8) = square root of (36 + 64) = square root of 100 = 10 km.
• Answer: 10 km (North-East of start).

Example 2: A girl walks 5 km East, 5 km West, then 3 km North.

• East-West: 5 East - 5 West = 0 net. North-South: 3 km North.
• Displacement = 3 km North.
• Answer: 3 km North of starting point.

• Adding all distances together instead of finding net displacement — total path is not displacement.
• Forgetting to cancel opposite directions before applying Pythagoras.
• Applying Pythagoras when moves are in the same direction (e.g., both North) — just add them directly.

1. A person walks 4 km South and then 3 km West. What is the displacement from the starting point?
2. A person walks 10 km North, then 10 km South. What is the displacement?