Final answer:
The ant's displacement relative to its original position can be found by adding the individual vectors representing its movements. The magnitude of the displacement vector is the length of the line connecting the origin to the final position of the ant. In this case, the magnitude is sqrt(850) cm.
Step-by-step explanation:
To find the ant's displacement relative to its original position, we can treat each segment of the ant's path as a vector. The eastward movement can be represented as a vector of magnitude 30 cm in the positive x-direction. The northward movement can be represented as a vector of magnitude 25 cm in the positive y-direction. The westward movement can be represented as a vector of magnitude 15 cm in the negative x-direction. To find the ant's displacement, we can add these vectors together using the graphical technique for adding vectors.
Start by drawing the eastward vector from the origin (0,0) to (30,0), then draw the northward vector from the end of the eastward vector to (30,25). Finally, draw the westward vector from the end of the northward vector to (30-15,25). The displacement vector from the origin to the final position of the ant is the resultant vector obtained by connecting the origin to the end point of the westward vector.
Using the Pythagorean theorem, we can find the magnitude of the displacement vector. The magnitude is the square root of the sum of the squares of the x and y components of the vector. In this case, the x component is 30-15 = 15 cm and the y component is 25 cm. Using the formula, the magnitude of the displacement vector is sqrt((15)^2 + (25)^2) = sqrt(225 + 625) = sqrt(850) cm.