Answer to Question #179014 in Classical Mechanics for Dylan

Question #179014

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?


1
Expert's answer
2021-04-08T08:52:02-0400

"\\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




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