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 5.4 km, but when the snow clears, he discovers that he actually traveled 8.0 km at 45o north of due east. (a) How far and (b) in what direction (south of due west) must he now travel to reach base camp? 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 5.4 km, but when the snow clears, he discovers that he actually traveled 8.0 km at 45o north of due east. (a) How far and (b) in what direction (south of due west) must he now travel to reach base camp?

Explanation / Answer

a) let north be y direction and east to x direction.
actual displacement.
y=8*sin45
x=8*cos45
so distance to the base came.
(y-5.4)^2+x^2=r^2
so r=5.65(km)
b) vector of direction.
(0,5.4)-(8*cos45,8*sin45)=(-5.6,-6.5).
so the angle 0
tan0 = -6.5/-5.6
so 0 = 49.23(deg) (from east)

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