Solving Aditi's Movement Puzzle

This solution explains how to determine the direction and distance of Aditi's home from her final location after a series of movements. We will use a coordinate system to track her path accurately.

Setting Up the Coordinate System

To visualize Aditi's journey, we can use a standard Cartesian coordinate system:

• Let Aditi's home be the origin (0, 0).
• The positive y-axis represents North.
• The negative y-axis represents South.
• The positive x-axis represents East.
• The negative x-axis represents West.

Tracking Aditi's Movements Step-by-Step

We will break down each part of Aditi's walk and note her position and direction:

Calculating Aditi's Final Position

After completing all five steps, Aditi's final position is (-24, 0).

This means her final location is 24 meters West of her starting point (home).

Finding Home's Location Relative to Final Position

The question asks for the direction and distance of her home from her final position.

• Aditi's Home Position (\(P_{home}\)) = (0, 0)
• Aditi's Final Position (\(P_{final}\)) = (-24, 0)

To find the location of home relative to the final position, we calculate the displacement vector from the final position to the home position:

Displacement Vector \(\vec{d} = P_{home} - P_{final}\)

We use LaTeX for the calculation:

\(\vec{d} = (0, 0) - (-24, 0)\)

Subtracting the coordinates:

\(\vec{d} = (0 - (-24), 0 - 0)\)

\(\vec{d} = (24, 0)\)

Interpreting the Result

The resulting displacement vector is \(\vec{d} = (24, 0)\).

• The x-component is \(+24\). This signifies a movement of 24 meters towards the East (positive x-direction).
• The y-component is \(0\). This signifies no movement needed in the North-South direction.

The distance is the magnitude of this vector:

Distance \(= \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(24)^2 + (0)^2} = \sqrt{576} = 24\) meters.

Therefore, Aditi's home is located 24 meters East from her final position.