Answer :
Answer:
Magnitude of the hiker's total displacement = 3.5 km
Angle and direction of the hiker's total displacement = 22 degree south of west
Explanation:
The first Displacement in vector form is
[tex]s_1[/tex] = -4.5 cos 45i +4.5 sin 45j
= -3.182i + 3.182j
The second Displacement in vector form is
[tex]s_2[/tex]= -4.5j
The total displacement is ,
[tex]s = s_1+ s_2[/tex]
= -3.182i + 3.182j - 4.5j
=-3.182i-1.318j
The magnitude of the displacement is,
[tex]s= \sqrt{(-3.182)^2 + (-1.318)^2\\[/tex]
[tex]s=\sqrt{10.125+1.7371}[/tex]
[tex]s=\sqrt{11.862}[/tex]
s= 3.444
The direction is,
[tex]\theta = tan^{-1}(\frac{1.318}{3.182})[/tex]
[tex]\theta = tan^{-1}(0.4142)[/tex]
[tex]\theta = 22.49^{\circ}[/tex]