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 8.5 km at 54o north of due east. (a) how far and (b) in what direction (south of due west) must he now travel to reach base camp?

(a) He must travel 5.25 km

(b) 17.7° south of west

Step-by-step explanation:

(Please see attached file)

1. He was supposed to travel 5.3 km due north to return to base camp

(vector S)

S = (Sx, Sy)

Sx= 0

Sy= 5.3

2. He discovers that he actually traveled 8.5 km at 54° north of due east (vector D)

D= (Dx, Dy)

Dx= Dcos Ф = 8.5cos54° = 5.0

Dy= Dsen Ф = 8.5sen54° = 6.9

3. He now needs to reach the base camp. Then, we need to find vector R.

From vectors addition/subtraction:

S = D + R

R = S - D

R= (Rx, Ry)

Rx = Dx - Sx = 0 - 5.0 = -5.0

Ry = Dy - Sy = 5.3 - 6.9 = -1.6

Magnitude of R =

Magnitude of R =

Magnitude of R = 5.25 km

Direction:

tanβ =

tanβ =

tanβ = 0.32

β = tan-1 (0.32)

β= 17.7° south of west

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