Question

A postman was returning to the post office, which was in front of him to the north. When the post office was 100 m away from him, he turned to the left and moved 50 m to deliver the last letter at Shanti Villa. He then moved in the same direction for 40 m, turned to his right, and moved 100 m. How many meters was he away from the post office?

Answer 1

The postman is approximately 180.28 m away from the post office after following a series of movements.

Step-by-step explanation:

The postman's movement can be represented using vectors. Let's break down the postman's movements:

1. The postman moves 100 m to the north to reach the post office.
2. The postman turns left and moves 50 m to deliver the last letter at Shanti Villa.
3. The postman continues in the same direction for 40 m.
4. Then, the postman turns right and moves 100 m.

To determine the postman's distance from the post office, we need to find the net displacement.

Net Displacement = Final Position - Initial Position

Using vector addition, we can calculate the net displacement:

Net Displacement = (100 m north) + (50 m west) + (40 m west) + (100 m north)

Net Displacement = 100 m north + 150 m west

The postman is 100 m north and 150 m west from the post office, which forms a right-angled triangle. We can use Pythagoras' theorem to find the distance from the post office.

Distance = √((100 m)^2 + (150 m)^2)

Distance = √(10000 m^2 + 22500 m^2)

Distance = √(32500 m^2)

Distance ≈ 180.28 m

Therefore, the postman is approximately 180.28 m away from the post office.