Question

A man walks 4 km West and turns right to walk 3 km. Where is he now from the starting point?

• A. 4 km North
• B. 5 km North-West
• C. 5 km North-East
• D. 3 km East

Hint:

Use Pythagoras theorem for perpendicular movement problems.

Answer 1

The Correct Option is B

To solve this problem, we need to determine the final position of the man from the starting point after making the described moves. Let's break down the steps:

1. Initial Movement: The man starts at a point, say O. He walks 4 km towards the west. Let's denote his position after this movement as A.
2. Second Movement: From point A, he turns right and walks 3 km. Since he was initially heading west, turning right would direct him towards the north. Let's denote his final position as B.
3. Determine the Distance from the Starting Point: We need to find the distance OB (from the start to the final position). Since the man moves west and then north, the path forms a right-angled triangle at A, with OA = 4 km and AB = 3 km.
   • Applying the Pythagorean theorem to triangle OAB: \(OB = \sqrt{(OA)^2 + (AB)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ km}\)
4. Determine the Direction: As he moved west and then north, his final position north-west of the starting point O.
5. Conclusion: The man is 5 km away in the north-west direction from the starting point.

The correct answer is 5 km North-West.