Question

using a ruler, draw a fully labeled vector scale diagram to determine the resultant displacement in the horizontal direction and another fully labeled vector scale diagram to determine the resultant displacement in the vertical direction.
horizontal:
1 cm: 4 m

δd

_ab = 11.4 m e

δd

_cd = 27.6 m e

|δd|_m = 39.0 m e
vertical:
1 cm: 4 m
|δd|_ef = 8.6 m s
|δd|_gh = 34.4 m s

Explanation:

Step1: Identify horizontal displacements

We have $\Delta d_{AB}=11.4\ cm$ [E] and $\Delta d_{CD}=27.6\ cm$ [E]. The scale is $1\ cm:4\ m$.

Step2: Calculate horizontal resultant displacement

First, convert each displacement to actual - distance. $\Delta d_{AB - actual}=11.4\times4 = 45.6\ m$ [E] and $\Delta d_{CD - actual}=27.6\times4=110.4\ m$ [E]. The horizontal resultant $\Delta d_{h - actual}=\Delta d_{AB - actual}+\Delta d_{CD - actual}=45.6 + 110.4=156\ m$ [E].

Step3: Identify vertical displacements

We have $\Delta d_{EF}=8.6\ cm$ [S] and $\Delta d_{GH}=34.4\ cm$ [S]. The scale is $1\ cm:4\ m$.

Step4: Calculate vertical resultant displacement

Convert each displacement to actual - distance. $\Delta d_{EF - actual}=8.6\times4 = 34.4\ m$ [S] and $\Delta d_{GH - actual}=34.4\times4 = 137.6\ m$ [S]. The vertical resultant $\Delta d_{v - actual}=\Delta d_{EF - actual}+\Delta d_{GH - actual}=34.4+137.6 = 172\ m$ [S].

Answer:

Horizontal resultant displacement: $156\ m$ [E]
Vertical resultant displacement: $172\ m$ [S]