In reaching her destination, a backpacker walks with an average velocity of 1.26 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.60 m/s, due west, turns around, and hikes with an average velocity of 0.470 m/s, due east. How far east did she walk?
Let x be the distance she walked due East.
Then
Total displacement, D = 6.44-x
Total time, T = 6.44/2.6 + x/0.47
D = 1.26*T
Solve for x. I get about 0.9 km.
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To find the distance the backpacker walked east, we can calculate the total displacement and subtract the distance walked west.
First, let's find the distance walked west. We can use the formula:
distance = velocity * time
The time it took for the backpacker to walk west can be calculated by dividing the distance by the velocity:
time = distance / velocity
Using this, we can find the time taken to walk west:
time walked west = 6.44 km / 2.60 m/s
Converting the distance to meters and calculating:
time walked west = 6.44 km × 1000 m/km / 2.60 m/s = 2476.92 s
Next, we need to find the distance walked east. We can use the same formula:
distance = velocity * time
The time it took for the backpacker to walk east can be calculated as:
time walked east = 2476.92 s (since the total time is the same)
Now, we can use the average velocity to find the distance walked east:
distance walked east = average velocity * time walked east
Calculating:
distance walked east = 0.470 m/s * 2476.92 s
distance walked east ≈ 1163.33 m
Therefore, the backpacker walked approximately 1163.33 meters east.