Decoding Rohan's Directional Movement

This problem requires us to trace a path involving sequential movements and turns to determine the final direction relative to the starting point. Let's break down Rohan's journey step-by-step.

Tracking Rohan's Path

We need to follow Rohan's movements precisely:

• Initial Movement: Rohan starts by walking 10 meters directly towards the North.
• First Turn and Movement: He then makes a right turn. Facing North, a right turn means he is now oriented towards the East. He proceeds to walk 5 meters in this direction.
• Second Turn and Movement: Again, Rohan turns right. Having been facing East, this turn orients him towards the South. He then walks 10 meters towards the South.

Analyzing Net Displacement

To find his final direction from the starting point, we analyze the net effect of his movements:

• North-South Movement: Rohan first moved 10 meters North and later moved 10 meters South. These movements are in opposite directions and cover the same distance. Therefore, they effectively cancel each other out in terms of North-South displacement. His final North-South position is the same as his starting position.
• East-West Movement: The only movement Rohan made in the East-West dimension was the 5 meters he walked towards the East after his first right turn.

Combining these, Rohan's net displacement is 5 meters towards the East from his starting point.

Final Direction Determination

Since Rohan's North-South position relative to the start is unchanged, and he is 5 meters East of his starting point, his final direction from the starting point is unequivocally East.

Let's use a coordinate system to visualize this, assuming the starting point is the origin (0, 0):

• Starting Point: (0, 0)
• After walking 10m North: Position becomes (0, 10). Rohan is facing North.
• After turning right (now facing East) and walking 5m: Position becomes (5, 10). Rohan is facing East.
• After turning right (now facing South) and walking 10m: Position becomes (5, 0). Rohan is facing South.

The final coordinates (5, 0) indicate a position 5 units along the positive x-axis relative to the origin (0, 0). In directional terms, this is 5 meters to the East.