Question

a giraffe trots 3.40 km due north, then 2.60 km due west. what is the magnitude of its displacement?

Explanation:

Step1: Use Pythagorean theorem

The north - south and west - east displacements are perpendicular. Let the north - ward displacement $a = 3.40$ km and the west - ward displacement $b=2.60$ km. The magnitude of the net displacement $d$ is given by $d=\sqrt{a^{2}+b^{2}}$.

Step2: Substitute values

Substitute $a = 3.40$ and $b = 2.60$ into the formula: $d=\sqrt{(3.40)^{2}+(2.60)^{2}}=\sqrt{11.56 + 6.76}=\sqrt{18.32}$.

Step3: Calculate the result

$\sqrt{18.32}\approx4.28$ km.

Answer:

$4.28$ km