An explorer is caught in a whiteout (in which the snowfall is so thick that the

Question

An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. He was supposed to travel due north for 5.3 km, but when the snow clears, he discovers that he actually traveled 8.2 km at 52o north of due east. (a) How far and (b) in what direction (south of due west) must he now travel to reach base camp?

This answer has no units° (degrees)kmkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3times

Explanation / Answer

Given that

vector A=5.3j

vector B=(8.2cos52)i+(8.2sin52) j=5.05 i+6.5 j

now we find the resultant displacement

resultant displacement S=(5.05)i+(5.3+6.5)j=5.05i+11.8j

displacent s=[5.05^2+11.8^2]^1/2=12.8 km

direction =tan^-1[11.8/5.05]=66.8 degree

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