To calculate the total displacement, we treat this as a three-dimensional vector problem. The body moves in three perpendicular directions: north, east, and vertically upward.

Step-by-Step Breakdown:

1. Movement Towards North (10 m):

   • This movement happens along the y-axis.
   • So, the displacement vector for this part is: $\vec{r_1} = 0\hat{i} + 10\hat{j} + 0\hat{k}$.

2. Movement Towards East (15 m):

   • This movement happens along the x-axis.
   • So, the displacement vector for this part is: $\vec{r_2} = 15\hat{i} + 0\hat{j} + 0\hat{k}$.

3. Movement Vertically Upward (20 m):

   • This movement happens along the z-axis.
   • So, the displacement vector for this part is: $\vec{r_3} = 0\hat{i} + 0\hat{j} + 20\hat{k}$.

Total Displacement:

The total displacement vector is the vector sum of all the individual displacement vectors:

= (0\hat{i} + 10\hat{j} + 0\hat{k}) + (15\hat{i} + 0\hat{j} + 0\hat{k}) + (0\hat{i} + 0\hat{j} + 20\hat{k})$$ $$\vec{r_{total}} = 15\hat{i} + 10\hat{j} + 20\hat{k}$$ Now, the **magnitude** of the total displacement is given by the formula for the magnitude of a vector: $$|\vec{r_{total}}| = \sqrt{(15)^2 + (10)^2 + (20)^2}$$ $$|\vec{r_{total}}| = \sqrt{225 + 100 + 400} = \sqrt{725}$$ $$|\vec{r_{total}}| \approx 26.93 \, \text{m}$$ ### Final Answer: The total displacement is approximately **26.93 meters**. Would you like more details on this, or do you have any further questions? Here are some related questions for you to consider: 1. How do you calculate displacement in a two-dimensional plane (like just North and East)? 2. What is the difference between distance and displacement? 3. How would you calculate displacement if the body moved in a circular path? 4. How would the displacement change if there was an additional movement in the south direction? 5. What is the role of vectors in calculating displacement in physics? **Tip:** Remember that displacement is always the shortest straight-line distance between the initial and final positions, and it can be represented as a vector.