Solving the Direction and Distance Problem

This problem involves tracking the movement of an animal from a starting point A through a series of turns and distances. To find the final position relative to the start, we need to calculate the net displacement in the East-West direction and the North-South direction separately.

Understanding the Animal's Movement

Let's break down the animal's journey step-by-step from starting point A:

1. Walked 15 m towards East.
2. Took a left turn (now facing North) and walked 25 m (towards North).
3. Took a right turn (now facing East) and walked 10 m (towards East).
4. Again took a left turn (now facing North) and walked 15 m (towards North).
5. Finally took a left turn (now facing West) and walked 25 m (towards West).

Calculating Net Displacement

We can sum the movements in the same direction and subtract movements in opposite directions.

East-West Displacement:

• Initial movement: 15 m East
• Third movement: 10 m East
• Fifth movement: 25 m West

Total Eastward movement = \(15 \text{ m} + 10 \text{ m} = 25 \text{ m}\)

Total Westward movement = \(25 \text{ m}\)

Net East-West displacement = Total Eastward movement - Total Westward movement

Net East-West displacement = \(25 \text{ m East} - 25 \text{ m West}\)

Net East-West displacement = \(0 \text{ m}\)

This means the animal's final East-West position is the same as its starting East-West position.

North-South Displacement:

• Second movement: 25 m North
• Fourth movement: 15 m North

Total Northward movement = \(25 \text{ m} + 15 \text{ m} = 40 \text{ m}\)

There was no Southward movement.

Net North-South displacement = Total Northward movement - Total Southward movement

Net North-South displacement = \(40 \text{ m North} - 0 \text{ m South}\)

Net North-South displacement = \(40 \text{ m North}\)

Determining Final Position from Starting Point A

The animal's final position relative to the starting point A is determined by the net displacements:

• Net East-West displacement: 0 m
• Net North-South displacement: 40 m North

Since the net East-West displacement is 0 m, the animal is directly North of the starting point A. The distance North is 40 m.

Therefore, the animal is 40 m, North from the starting point A.

Conclusion

By calculating the total movement in the East/West and North/South directions, we found the net displacement. The net displacement was 0 m horizontally (East/West) and 40 m vertically (North). This places the animal 40 m North of its starting point A.

The net displacement is 0 m East/West and +40 m North. This means the final position is 40 m North of the start.

Revision Table: Key Concepts

Additional Information: Solving Direction Problems

Solving direction and distance problems like this often involves breaking down movements into components along perpendicular axes, typically North-South and East-West. Here are some tips:

• Visualize: Imagine or sketch the path taken.
• Assign Directions: Standard convention is North up, South down, East right, West left on a map.
• Components: Separate all movements into their East/West components and North/South components.
• Net Movement: Sum the distances in the same direction (e.g., all Eastward movements) and subtract distances in the opposite direction (e.g., subtract Westward from Eastward).
• Final Position: The resulting net East/West and North/South displacements tell you the final position relative to the start. If net East/West is zero, the final position is directly North or South. If net North/South is zero, it's directly East or West. If both are non-zero, you'd use the Pythagorean theorem to find the direct distance and trigonometry to find the direction (though not needed in this specific problem).

Left and right turns are crucial. A left turn changes direction 90 degrees counter-clockwise, and a right turn changes direction 90 degrees clockwise from the current facing direction.