Question

Ms. Ratchford wants to go for a walk. She travels to Starbucks which is 2km [N30E] she then goes to Walmart to get groceries and travels 500m [E10S]. What is her displacement?

Answer 1

$\text{we write each move (travel) as a vector whose coordinates}$

$\text{are projections onto S,N,W,E}$

$\vec{T_1}(2000*\cos30\degree \vec{N};2000*\sin30\degree \vec{E})$

$\vec{T_1}(1732 \vec{N};1000 \vec{E})$

$\vec{T_2}(500*\sin10\degree \vec{S};500*\cos10\degree \vec{E})$

$\vec{T_2}( 86.8\vec{S};492.4\vec{E})$

$\vec{S}=-\vec{N}$

$\vec T = \vec T_1+\vec T_2$

$\vec T((1732-86.8)\vec S;(1000+492.4)\vec E)$

$\vec T(1645.2\vec S;1492.4\vec E)$

$|\vec T| = \sqrt{1645.2^2+1492.4^2}=2221.2$

Answer: displacement 2221.2m