Aman's House Directional Movement Breakdown

The goal is to determine the straight-line distance between Aman's starting position and his final stopping point after following a sequence of movements. We need to carefully analyze each step involving direction and distance.

• Initial Position Context: Aman's house door faces East. This implies the rear or back side of his house faces the opposite direction, which is West.
• Movement 1: Aman begins by walking straight from the back side of his house for 30m. Since the back side is West, this first movement is 30m West.
• Movement 2: Next, he turns to his left. If Aman is facing West, a left turn orients him towards the South. He then walks 20m South.
• Movement 3: Subsequently, he turns to his right. From facing South, a right turn means he is now facing West. He covers a distance of 30m West.
• Movement 4: Finally, Aman changes direction to face North and walks 20m North before stopping.

Calculating Net Displacement Westward

To find the final distance, we must calculate Aman's total displacement. This involves summing up all movements along the East-West axis and the North-South axis separately.

• Total Displacement along the East-West Axis: Aman makes two movements towards the West.
  • The first movement is 30m West.
  • The second movement is 30m West.
  Combining these, the total displacement towards the West is calculated as: $30m_{West} + 30m_{West} = 60m_{West}$.
• Total Displacement along the North-South Axis: Aman moves South and then North.
  • Movement South: 20m
  • Movement North: 20m
  The net displacement in the North-South direction is calculated by subtracting the Northward movement from the Southward movement: $20m_{South} - 20m_{North} = 0m$. This indicates that his final North-South position is the same as his starting North-South position.

Final Distance Between Start and End Points

With the net displacement in the North-South direction being zero, Aman's final position relative to his start is solely determined by his total movement along the East-West axis.

His overall displacement from the starting point is therefore 60m West.

The distance between the starting point and the end point is the magnitude of this net displacement. It represents the shortest straight-line path from the beginning to the end.

Thus, the distance between the starting and end point is 60m.