A student walks from the ground floor up to the fourth floor of a building and then down to the second floor. Each floor is 3 m high. Calculate (i) the total vertical distance travelled and (ii) their

The height of each floor is $3 \text{ m}$.

• Ground floor (starting point): $0 \text{ m}$
• Second floor (classroom): $2 \times 3 \text{ m} = 6 \text{ m}$
• Fourth floor: $4 \times 3 \text{ m} = 12 \text{ m}$

The student's journey has two segments:

• From the ground floor to the fourth floor: Distance travelled upwards = $12 \text{ m} - 0 \text{ m} = 12 \text{ m}$
• From the fourth floor down to the second floor: Distance travelled downwards = $12 \text{ m} - 6 \text{ m} = 6 \text{ m}$

The total vertical distance travelled is the sum of the magnitudes of these distances.

$$\text{Total vertical distance} = 12 \text{ m} + 6 \text{ m}$$ $$\text{Total vertical distance} = 18 \text{ m}$$

Displacement is the change in position from the starting point to the final point.

• Starting point: Ground floor ($0 \text{ m}$)
• Final point: Second floor ($6 \text{ m}$)

$$\text{Displacement} = \text{Final position} - \text{Starting position}$$ $$\text{Displacement} = 6 \text{ m} - 0 \text{ m}$$ $$\text{Displacement} = 6 \text{ m}$$

The displacement is $6 \text{ m}$ upwards from the starting point.

(i) The total vertical distance travelled is $\boxed{\text{18 m}}$.

(ii) Their displacement from the starting point is $\boxed{\text{6 m}}$.