A person starts from his house, travels a distance of 12 m westwards, then travels a distance of 10 m northwards, then a distance of 10 m eastwards, then a distance of 10 m southwards. What is his distance from his house at present ?

Explanation

Movements:

1. 12 meters west
2. 10 meters north
3. 10 meters east
4. 10 meters south

Calculations:

East-West Direction:

• Starts at 0 meters.
• Moves 12 meters west: 0 - 12 = -12 meters.
• Moves 10 meters east: -12 + 10 = -2 meters.
• Net displacement in the east-west direction: -2 meters (2 meters west).

North-South Direction:

• Starts at 0 meters.
• Moves 10 meters north: 0 + 10 = 10 meters.
• Moves 10 meters south: 10 - 10 = 0 meters.
• Net displacement in the north-south direction: 0 meters.

Net Displacement Vector:

• East-West: -2 meters.
• North-South: 0 meters.

The magnitude of the displacement is calculated using the Pythagorean theorem:

Displacement = sqrt((-2)² + 0²) = sqrt(4) = 2 meters 

Final Answer

The person's current distance from their house is 2 meters.