While John is traveling along a straight interstate
highway, he notices that the mile marker
reads 256 km. John travels until he reaches
the 144 km marker and then retraces his path
to the 173 km marker.
What is John’s resultant displacement from
the 256 km marker?
How far has he traveled?
distance traveled=(256-144)+(173-144))
displacement=(256-173)
To find John's resultant displacement from the 256 km marker, we need to calculate the distance between the 256 km marker and the 173 km marker. This can be found by subtracting the initial position from the final position.
Displacement = Final position - Initial position
Displacement = 173 km - 256 km
Displacement = -83 km
John's resultant displacement from the 256 km marker is -83 km. The negative sign indicates that he is traveling in the opposite direction.
To find the distance John has traveled, we need to calculate the sum of the distances from the 256 km marker to the 144 km marker and from the 144 km marker to the 173 km marker.
Distance = Distance1 + Distance2
= (256 km - 144 km) + (173 km - 144 km)
= 112 km + 29 km
= 141 km
Therefore, John has traveled a distance of 141 km.
To find John's resultant displacement from the 256 km marker, we need to find the difference between his ending point (the 173 km marker) and the starting point (the 256 km marker).
Resultant Displacement = Ending Point - Starting Point
Resultant Displacement = 173 km - 256 km
To subtract the two numbers, you have to borrow 1 from the hundreds place and add it to the tens place of the second number (173 km marker in this case). It becomes 173 + 900 km, which equals 1073 km.
Therefore, John's resultant displacement from the 256 km marker is 1073 km.
To find how far John has traveled, we need to add the distance he traveled in one direction to the distance he traveled back.
Distance traveled = Distance to 144 km marker + Distance from 144 km marker to 173 km marker
Distance traveled = 256 km - 144 km + 173 km - 144 km
Simplifying the equation, we have:
Distance traveled = 112 km + 29 km
Distance traveled = 141 km
Therefore, John has traveled a total distance of 141 km.