Question

a lady walked 254 m west, then 54 m north. what is the magnitude of her displacement? a 308 m b 67432 m c 13716 m d 260 m

Explanation:

Step1: Identify the right - angled triangle

The west - ward and north - ward displacements form the two legs of a right - angled triangle. Let the west - ward displacement $a = 254$ m and the north - ward displacement $b = 54$ m.

Step2: Apply the Pythagorean theorem

The magnitude of the displacement $d$ (the hypotenuse of the right - angled triangle) is given by $d=\sqrt{a^{2}+b^{2}}$. Substitute $a = 254$ and $b = 54$ into the formula: $d=\sqrt{254^{2}+54^{2}}=\sqrt{(254\times254)+(54\times54)}=\sqrt{64516 + 2916}=\sqrt{67432}\approx260$ m

Answer:

D. 260 m