I walk 30 metres in North-West direction from my house and then 30 metres in South-West direction. After this I walk 30 metres in South-East direction. Now, I turn to my house, in what direction am I going?

Correct option is D

Solution

We are tasked to determine the direction you are walking back to your house after following a specific set of movements.

Analysis:

1. From the house: You walk 30 meters in the North-West (NW) direction. This results in a displacement of:

$$30/\sqrt{2} \, \text{meters north}$$​

$$30/\sqrt{2} \, \text{meters west}$$​

2. Next movement: You walk 30 meters in the South-West (SW) direction. This results in:

$$30/\sqrt{2} \, \text{meters south}$$​

$$30/\sqrt{2} \, \text{meters west}$$​

Net displacement after first two movements:

- North-South: $$30/\sqrt{2} - 30/\sqrt{2} = 0 \, \text{(no net vertical displacement)}$$​

- East-West: $$30/\sqrt{2} + 30/\sqrt{2} = 60/\sqrt{2} = 30\sqrt{2} \, \text{meters west}$$​

3. Final movement: You walk 30 meters in the South-East (SE) direction. This results in:

$$30/\sqrt{2} \, \text{meters south}$$​

$$30/\sqrt{2} \, \text{meters east}$$​

Net displacement after all movements:

- North-South: $$0 - 30/\sqrt{2} = -30/\sqrt{2} \, \text{(south)}$$​

- East-West: $$30\sqrt{2} - 30/\sqrt{2} = 30/\sqrt{2} \, \text{(west)}$$​

Conclusion:

Your final position is $$30/\sqrt{2} \, \text{meters south} and 30/\sqrt{2} \, \text{meters west}$$​ of the house.

To return to the house, you must walk in the North-East direction.

Final Answer:

You are going in the North-East direction.