An explorer is caught in a whiteout (in which the snowfall is sothick that the g

Question

An explorer is caught in a whiteout (in which the snowfall is sothick that the ground cannot be distinguished from the sky) whilereturning to base camp. He was supposed to travel due north for4.2 km, but when the snow clears, hediscovers that he actually traveled 7.8 km at 48° north of due east. (a) How far must he now travel to reach basecamp?
1 km

(b) In what direction must he travel?
2°(counterclockwise from due east) (a) How far must he now travel to reach basecamp?
1 km

(b) In what direction must he travel?
2°(counterclockwise from due east)

Explanation / Answer

Use components to solve this, so first sum up the x components(using dx for the unknown x comp. to base) then 7.8kmCos48+dx=0 andfor the y components we have 7.8kmSin48-4.2km=dy, so dx= -5.22kmand dy=1.59 km, sod=(5.222+1.592)=5.46 km b) =tan-1(dy/dx)= 163 degrees

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