What is the hiker's total displacement?
part a of the hike: distance:4km east
start time: 9:00 am end time: 9:45 am
part b: distance:6 km south
start time: 9:45 am end time: 10:45 am part c: distance:4 km west
start time:10:45 am end time: 11:15
part d: distance 6 km north
start time:11:15 am end time: 12:00 pm
start at (0,0)
after (a): (4,0)
after (b): (4,-6)
after (c): (0,-6)
after (d): (0,0)
final position is back at the starting point.
To calculate the hiker's total displacement, we need to determine the net distance and direction traveled.
We can break down the hiker's journey into four parts:
Part A: The hiker traveled 4 km east. This can be represented as a displacement of +4 km in the east direction.
Part B: The hiker traveled 6 km south. This can be represented as a displacement of -6 km in the south direction.
Part C: The hiker traveled 4 km west. This can be represented as a displacement of -4 km in the west direction.
Part D: The hiker traveled 6 km north. This can be represented as a displacement of +6 km in the north direction.
To calculate the total displacement, we can add up the individual displacements:
Total displacement = Part A + Part B + Part C + Part D
Total displacement = (+4 km) + (-6 km) + (-4 km) + (+6 km)
Adding these values, we get:
Total displacement = +4 km - 6 km - 4 km + 6 km
Total displacement = 0 km
Therefore, the hiker's total displacement is 0 km.