Answer to Question #208483 in Mechanics | Relativity for Coleman

Question #208483

A man start from a point A and walk a distance of 8.0 km due northeast to point B from B he then walks 4.0 km due South East to point x. Calculate the shortest distance between A and x.






1
Expert's answer
2021-06-18T11:21:56-0400

AX=AB+BX\vec{AX}=\vec{AB}+\vec{BX}

(AB,BX)=(NE,SE)=π2\angle(\vec{AB},\vec{BX})=\angle(\vec{NE},\vec{SE})=\frac{\pi}{2}

AX2=(AB+BX)2\vec{AX}^2=(\vec{AB}+\vec{BX})^2

AX2=AB2+BX2+2ABBX\vec{AX}^2=\vec{AB}^2+\vec{BX}^2+2\vec{AB}*\vec{BX}

2ABBX=2ABBXcos((AB,BX))=02\vec{AB}*\vec{BX}=2* AB*BX*\cos(\angle(\vec{AB},\vec{BX}))=0

AX2=AB2+BX2AX^2 =AB^2+BX^2

AX=AB2+BX2=82+42=8.94AX =\sqrt{AB^2+BX^2}=\sqrt{8^2+4^2}=8.94

Answer : AX=8.94 km\text{Answer : }AX =8.94\ km




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