Answer:
To find the magnitude of Vanessa’s displacement, we need to use the displacement formula and the Pythagorean theorem.
The displacement formula is given by: S = Sf – Si, where S is the displacement, Sf is the final position and Si is the initial position of the object.
The Pythagorean theorem states that in any right triangle, the sum of the squares of the lengths of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse. This theorem is represented by the formula a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse of the right triangle.
In this case, Vanessa’s initial position is the origin, and her final position is after walking northward and eastward. Therefore, her displacement vector is S = (180, 169) - (0, 0) = (180, 169).
To find the magnitude of her displacement, we need to use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by her displacement vector and the x- and y-axes. The legs of the triangle are 180 m and 169 m, so the hypotenuse is c = √(180^2 + 169^2) = √(32400 + 28561) = √60961 ≈ 246.91 m.
Therefore, the magnitude of Vanessa’s displacement is 246.91 m.