Understanding the Direction and Distance Problem

This question asks us to determine Gaurav's final position relative to his starting point after a series of movements involving specific distances and turns. It's a classic direction and distance problem that requires careful tracking of movement along the cardinal directions: North, South, East, and West.

Step-by-Step Movement Analysis

Let's break down Gaurav's path step by step. His house faces North, and he exits from the backdoor. Exiting the backdoor of a North-facing house means he starts moving in the South direction.

1. Initial Movement: He walks 25 m straight after exiting the backdoor. Since the backdoor is opposite the front (North-facing), his initial movement is 25 m South.
2. First Turn: He takes a left turn. From South, a left turn is towards the East. He walks 36 m East.
3. Second Turn: He turns left again. From East, a left turn is towards the North. He walks 47 m North.
4. Third Turn: He turns left again. From North, a left turn is towards the West. He walks 36 m West.

Calculating Net Displacement

To find his final position relative to his starting point (the backdoor), we need to calculate the net displacement in the North-South direction and the East-West direction.

Net East-West Displacement

• He walked 36 m East.
• Then he walked 36 m West.
• The net East-West displacement is $36 \, \text{m (East)} - 36 \, \text{m (West)} = 0 \, \text{m}$.
• This means he is neither East nor West of his starting point; he is directly inline vertically with it.

Net North-South Displacement

• He initially walked 25 m South.
• Then he walked 47 m North.
• The net North-South displacement is $47 \, \text{m (North)} - 25 \, \text{m (South)}$.
• $47 - 25 = 22 \, \text{m}$. Since the North movement (47 m) was greater than the South movement (25 m), the net displacement is 22 m in the North direction.

Determining Final Position Relative to House

Combining the net displacements:

• Net East-West displacement: 0 m
• Net North-South displacement: 22 m North

Therefore, Gaurav is 22 m North of his starting point (the backdoor of his house).

We can summarize the movements in a table:

His final position is 22 m North and 0 m East/West from his starting point. So, he is 22 m North from his house.

Concluding the Answer

Based on our analysis of Gaurav's direction and distance covered, his final position is 22 m North from where he started (the backdoor of his house).

Revision Table: Checking the Steps

Movements: 25m South, 36m East, 47m North, 36m West.

Net South = 25m

Net North = 47m

Net East = 36m

Net West = 36m

Net North/South: $47 - 25 = 22$ m North

Net East/West: $36 - 36 = 0$ m East/West

Final position: 22 m North of the start.

Additional Information on Direction Problems

Direction and distance questions often involve visualizing movements on a standard compass rose (North, South, East, West). Key points to remember:

• Relative Turns: "Left" and "Right" turns depend on the current direction of travel.
  • From North: Left is West, Right is East.
  • From South: Left is East, Right is West.
  • From East: Left is North, Right is South.
  • From West: Left is South, Right is North.
• Net Displacement: To find the final position relative to the start, sum up movements in opposite directions (North vs. South, East vs. West). The difference gives the net displacement in the direction of the larger value.
• Pythagoras Theorem: Sometimes, the final position might require calculating the diagonal distance using the Pythagorean theorem if there are non-zero net displacements in both perpendicular directions (e.g., net North and net East). In this problem, the net East-West displacement was zero, simplifying the calculation.