Answer:
a
The hiker (you ) is 200 m below his/her(your) starting point
b
The resultant displacement in the north east direction is
[tex]a = 6562.0 \ m [/tex]
The resultant displacement in vertical direction (i.e the altitude change )
[tex]b =6503.1 \ m [/tex]
Explanation:
From the question we are told that
The displacement in the morning is [tex]S_{morning} = (2200 \m , east) + (4000\ m\ north) + (100 \ m ,\ vertical)[/tex]
The displacement in the afternoon is [tex]S _{afternoon}= (1300\ m ,\ west) + (2500 \ m ,\ north) - (300\ m ,\ vertical)[/tex]
Generally the direction west is negative , the direction east is positive
the direction south is negative , the direction north is positive
resultant displacement is mathematically evaluated as
[tex](2200 \m , east) +( - 1300\ m ,\ west) = 900 \ m \ east[/tex]
[tex](4000\ m\ north) + (2500 \ m ,\ north) = 6500 \ m ,\ north[/tex]
[tex](100 \ m ,\ vertical) - (300\ m ,\ vertical) = -200 \ m[/tex]
From the above calculation we see that at the end of the hiking the hiker (you) is 200 m below his/her(your) initial position
Generally from Pythagoras theorem , the resultant displacement in the north east direction is
[tex]a = \sqrt{900^2 + 6500^2}[/tex]
=> [tex]a = 6562.0 \ m [/tex]
Generally from Pythagoras theorem , the resultant displacement in vertical direction (i.e the altitude change )
[tex]b = \sqrt{6500^2 +(-200)^2 }[/tex]
=> [tex]b =6503.1 \ m [/tex]
