Understanding Kedar's Journey and Distance Calculation

The problem asks us to find the final distance of Kedar from his starting point after a series of movements in different directions. This is a typical directional distance problem where we need to track the displacement from the origin.

Step-by-Step Analysis of Kedar's Movement

1. Kedar starts from his house and travels 25 km towards the south. Let's assume his starting point is the origin (0,0) on a coordinate plane. Traveling south takes him to the point (0, -25).
2. He then takes a left turn. If he is facing south, a left turn means turning towards the east. He travels 15 km towards the east. From (0, -25), traveling 15 km east takes him to the point (0 + 15, -25) = (15, -25).
3. He takes a left turn again. If he is facing east, a left turn means turning towards the north. He travels 25 km towards the north. From (15, -25), traveling 25 km north takes him to the point (15, -25 + 25) = (15, 0).

His final position is (15, 0) assuming his starting point (house) was (0, 0).

Calculating Distance from Original Position

The original position was the starting point (0, 0). The final position is (15, 0).

To find the distance between the starting point and the final position, we can use the distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \), which is \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Here, \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (15, 0) \).

Distance = \( \sqrt{(15 - 0)^2 + (0 - 0)^2} \)

Distance = \( \sqrt{(15)^2 + (0)^2} \)

Distance = \( \sqrt{225 + 0} \)

Distance = \( \sqrt{225} \)

Distance = 15 km.

Alternatively, we can visualize the movements:

• He went 25 km south and then 25 km north. These two movements cancel each other out in the north-south direction. His net displacement in the north-south direction is 0.
• He only had a movement of 15 km towards the east.

So, his final position is directly east of his starting point, at a distance equal to his eastward travel.

The distance from his original position is 15 km.

This matches one of the given options.

The final position is (15, 0). The distance from the origin (0, 0) is 15 km.

Revision Table: Key Concepts

Additional Information: Directional Problems

Directional sense problems often involve a series of movements in different directions. To solve them effectively, you can:

• Draw a diagram: Sketching the path helps visualize the movements and the final position relative to the start.
• Use coordinate geometry: Assigning the starting point as (0,0) and tracking the changes in x and y coordinates for each movement makes calculating the final position straightforward. Moving East increases the x coordinate, West decreases x, North increases y, and South decreases y.
• Understand turns: A left turn from North is West, from East is North, from South is East, and from West is South. Similarly for right turns.
• Differentiate between total distance traveled and displacement: Total distance is the sum of the lengths of all segments of the journey. Displacement is the shortest distance (a straight line) from the starting point to the ending point. This problem specifically asks "How far is he form his original position?", which implies displacement.

These methods help in accurately determining the final location and the distance from the origin for various directional travel scenarios.