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 4.9 km, but when the snow clears, he discovers that he actually traveled 7.8 km at 50° north of due east.

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 4.9 km, but when the snow clears, he discovers that he actually traveled 7.8 km at 50° north of due east.
(a) How far must he now travel to reach base camp?
(b) In what direction must he travel?

bobpursley · Answer

break the vectors down to components:

traveled: 7.8sin50 N + 7.8cos50E
Need to end up: 4.9N

Traveled+second leg=need to end up
7.8sin50N+7.8cos50E+SL=4.9N
SLeg=N(4.9-7.8sin50)- E7.8cos50

remember a negative direction is the opposite direction, as in - 5E=5W