In reaching her destination, a backpacker walks with an average velocity of 1.37 m/s, due west. This average velocity results, because she hikes for 6.62 km with an average velocity of 2.66 m/s due west, turns around, and hikes with an average velocity of 0.741 m/s due east. How far east did she walk (in kilometers)? Thank you!!
To find the distance walked in the eastward direction, we need to calculate the total displacement in that direction. Displacement is the difference between the initial position and final position.
First, we need to find the displacement for each leg of the journey.
For the first leg:
Distance = 6.62 km
Average velocity = 2.66 m/s (due west)
Using the formula:
Displacement = Distance × Direction
The displacement for the first leg can be calculated as:
Displacement1 = 6.62 km × (-1) (since west is considered negative)
Displacement1 = -6.62 km
For the second leg:
Average velocity = 0.741 m/s (due east)
Using the formula:
Displacement2 = Distance × Direction
We don't know the distance for the second leg, but since the backpacker turns around, we can assume that she covers the same distance. Therefore:
Displacement2 = Distance × (+1) (since east is considered positive)
Displacement2 = Distance (since Distance × 1 = Distance)
Now, to find the total displacement:
Total displacement = Displacement1 + Displacement2
Substituting the values, we have:
Total displacement = -6.62 km + Distance
Since the average velocity is the total displacement divided by the total time, we can use this to determine the time.
Total time = Total displacement / Average velocity
Total time = (-6.62 km + Distance) / 1.37 m/s
Now, we need to consider that the distance walked east, which resulted in Displacement2, is the same as the distance walked in the first leg:
Distance = 6.62 km
Substituting this back into the equation for Total time:
Total time = (-6.62 km + 6.62 km) / 1.37 m/s
Total time = 0 km / 1.37 m/s
Total time = 0 s
Since the total time obtained is zero, it means that the backpacker did not spend any time walking eastward. Therefore, the distance walked east is zero kilometers (0 km).