Question

A child is looking for his father. He went 90 metres in the East before turning to his right. He went 20 metres before turning to his right again to look for his father. He saw his uncle's place 30 metres from this point. His father was not there. From here he went 100 metres to the North before turning to his father's house. How far did the son reach from the starting point?

• A. 80 metres
• B. 100 metres
• C. 140 metres
• D. 200 metres
• E. 90 metres

Hint:

Break movement into horizontal and vertical components.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
We need to find the displacement (shortest distance) between the starting point and the final meeting point using the Pythagorean theorem.
Step 2: Detailed Explanation:
1. Start at $(0,0)$. Go East 90m: $(90, 0)$. 2. Turn Right (South) 20m: $(90, -20)$. 3. Turn Right (West) 30m: $(90-30, -20) = (60, -20)$. 4. Go North 100m: $(60, -20+100) = (60, 80)$.
Step 3: Calculation:
The distance from $(0,0)$ to $(60, 80)$ is calculated as: $$D = \sqrt{x^2 + y^2} = \sqrt{60^2 + 80^2}$$ $$D = \sqrt{3600 + 6400} = \sqrt{10000} = 100 \text{ metres}$$
Step 4: Final Answer:
The son met his father 100 metres from the starting point. Thus, the correct option is (b).