Answer:
(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 = [tex]\sqrt{Rx^{2}+Ry^{2} }[/tex]
Magnitude of R = [tex]\sqrt{(-5.0)^{2}+(-1.6)^{2} }[/tex]
Magnitude of R = 5.25 km
Direction:
tanβ = [tex]\frac{Ry}{Rx}[/tex]
tanβ = [tex]\frac{1.6}{5.0}[/tex]
tanβ = 0.32
β = tan-1 (0.32)
β= 17.7° south of west
