Answer to Question #210694 in Classical Mechanics for arslamst

Question

Ms. Ratchford wants to go for a walk. She travels to Starbucks which is 3.5 km [N11W] she then goes to Walmart to get groceries and travels 1.5 KM[S45E]. What is her displacement?

Answer 1

$\text{let:}$

$\text{point O starting point of movement}$

$\text{point S - Starbucks location}$

$\text{point W - Walmart location}$

$\alpha=\angle(\vec {OS},\vec {SW})$

$\alpha= [N11W] +\angle({\vec{N}},{\vec{E}})+ [S45E]=146\degree$

$\vec {OW}= \vec {OS}+\vec {SW}$

$|\vec {OW}|=\sqrt{|\vec {OS}|^2+|\vec {SW}|^2+2*|\vec {OS}|*|\vec {SW}|*\cos\alpha}$

$|\vec {OW}|=\sqrt{3.5^2+1.5^2+2*1.5*3.5*\cos146\degree}=2.4$

$\text{Aswer: displacement = 2.4 km}$