While John is traveling along a straight interstate highway, he notices that the mile marker reads 258 km. John travels until he reaches the 137 km marker and then retraces his path to the 176 km marker. 1) What is John’s resultant displacement from the 258 km marker? 2) How far has he traveled?
1) John's resultant displacement from the 258 km marker can be calculated by subtracting his final position (176 km marker) from his initial position (258 km marker). So, 258 km - 176 km = 82 km.
2) To calculate the distance John has traveled, we need to add his distance from the initial position to the final position. Here, John traveled from the 258 km marker to the 137 km marker and then back to the 176 km marker. So, the total distance traveled is 258 km - 137 km + 176 km = 297 km.
To determine John's resultant displacement from the 258 km marker, we need to calculate the difference between the distance he traveled in one direction (137 km) and the distance he traveled in the opposite direction (176 km).
1) Resultant displacement:
Displacement = Distance in one direction - Distance in opposite direction
Displacement = 137 km - 176 km
Displacement = -39 km
Therefore, John's resultant displacement from the 258 km marker is -39 km. The negative sign indicates that the displacement is in the opposite direction to his initial position.
2) Total distance traveled:
Total distance traveled is the sum of the distances covered in one direction and the distances covered in the opposite direction.
Distance traveled = Distance in one direction + Distance in opposite direction
Distance traveled = 137 km + 176 km
Distance traveled = 313 km
Therefore, John has traveled a total distance of 313 km.
To find John's resultant displacement from the 258 km marker, we need to consider both the distance he traveled away from the marker and the distance he traveled back towards it.
1) To calculate the displacement, we subtract the distance he traveled towards the marker from the distance he traveled away from it:
Displacement = Distance away - Distance towards
Distance away = 137 km
Distance towards = 258 km - 176 km = 82 km
Displacement = 137 km - 82 km = 55 km
Therefore, John's resultant displacement from the 258 km marker is 55 km.
2) To find how far John has traveled, we need to consider the total distance he covered from the starting point to the point where he turned back:
Total distance = Distance away + Distance towards
Distance away = 137 km
Distance towards = 82 km
Total distance = 137 km + 82 km = 219 km
Therefore, John has traveled a total distance of 219 km.
1. D = (137-258) + (258-137) + (176-258) = -121+121-82 = -82 km = 82 km
below 258 km marker.
2. d = 121+ 121+82 =