Complete Question
While john is traveling along a straight in interstate highway, he notices that the mile marker reads 242 km. John travels until he reaches the 147 km marker and then retraces his path to the 161 km marker. What is John's resultant displacement from the 242 km marker? How far has he traveled answer in units of km
Answer:
The resultant displacement [tex]\Delta x _{1 , 3} = 81 \ km[/tex]
The total distance traveled by john is [tex]x_t =109 \ km[/tex]
Explanation:
From the question we are told that
The first position of john from the finish point is [tex]x_1 = 242 \ km[/tex]
The second position of john from the finish point is [tex]x_2 = 147 \ km[/tex]
The third position of john from the finish point is [tex]x_3 = 161 \ km[/tex]
Generally the displacement from the 242 km marker is mathematically represented as
[tex]\Delta x _{1 , 3} = x_1 - x_3[/tex]
Here we used [tex]x_3[/tex] instead of [tex]x_2[/tex] because [tex]x_3[/tex] is further than [tex]x_2[/tex] from the finish point
=> [tex]\Delta x _{1 , 3} = 81 \ km[/tex]
Generally the total distance traveled by John is mathematically evaluated as
[tex]x_t = [x_1 - x_2 ] + [x_3 - x_2][/tex]
=> [tex]x_t = [242 - 147 ] + [161 - 147][/tex]
=> [tex]x_t =109 \ km[/tex]
