Understanding Udai's Walking Path

This question involves tracking a person's movement in different directions and calculating their final position relative to the starting point. We need to figure out the total displacement (distance and direction) from the start and then determine the path needed to reach a specific target point.

Step-by-Step Analysis of Udai's Walk

Let's break down Udai's journey step by step. We can consider the starting point as the origin (0,0) on a 2D plane, with East being the positive x-axis, West the negative x-axis, North the positive y-axis, and South the negative y-axis.

1. First Movement: Udai walks 25 m towards the west.
   • Starting Point: (0, 0)
   • Movement: 25 m West
   • Position after 1st step: \((-25, 0)\)
2. Second Movement: He turns left (South) and walks 55 m.
   • Current Position: \((-25, 0)\)
   • Movement: 55 m South
   • Position after 2nd step: \((-25, -55)\)
3. Third Movement: He takes a right turn (West) and walks 45 m.
   • Current Position: \((-25, -55)\)
   • Movement: 45 m West
   • Position after 3rd step: \((-25 - 45, -55) = (-70, -55)\)
4. Fourth Movement: He turns right again (North) and walks 70 m.
   • Current Position: \((-70, -55)\)
   • Movement: 70 m North
   • Position after 4th step: \((-70, -55 + 70) = (-70, 15)\)

Calculating Udai's Final Position

After all the movements, Udai's final position is at the coordinates \((-70, 15)\) relative to the starting point \((0, 0)\). This means he is 70 meters West and 15 meters North of where he started.

Determining the Target Location

The question asks about the movement needed to reach a point 15 m north of the starting point.

• Starting Point: \((0, 0)\)
• Target Point: 15 m North of the starting point
• Target Coordinates: \((0, 15)\)

Finding the Path to the Target

Udai is currently at \((-70, 15)\) and needs to reach \((0, 15)\). Let's see the change required in his coordinates:

• Change in x-coordinate: Target x - Current x = \(0 - (-70) = 0 + 70 = 70\)
• Change in y-coordinate: Target y - Current y = \(15 - 15 = 0\)

The required movement is \(+70\) in the x-direction and \(0\) in the y-direction.

• A positive change in the x-direction corresponds to movement towards the East.
• The change is 70 units.

Therefore, Udai should walk 70 meters towards the East to reach the target point.

Summary of Required Movement

To get from his final position \((-70, 15)\) to the target position \((0, 15)\), Udai must move 70 meters in the East direction.

Movement required from \((-70, 15)\) to \((0, 15)\) is \((0 - (-70), 15 - 15) = (70, 0)\).

This corresponds to a movement of 70 units in the positive x-direction, which is East.

Revision Table: Direction and Distance Concepts

Additional Information: Solving Direction Problems

Direction and distance problems are common in reasoning sections of exams. They test your spatial reasoning and ability to track movements.

• Visualisation: It helps to draw a diagram or visualize the path.
• Coordinate System: Using a coordinate system simplifies tracking the position relative to a fixed point (the start).
• Net Displacement: The final position relative to the start is the net displacement. It's the straight-line distance and direction from start to end.
• Relative Turns: "Left turn" and "Right turn" depend on the current direction of movement.
• Pythagoras Theorem: If the final position forms a right-angled triangle with the starting point, Pythagoras theorem can be used to find the straight-line distance. In this specific problem, the final position and target have the same y-coordinate, making the final movement purely horizontal.

Practicing different types of directional problems helps build confidence in handling turns and multiple movements.