In reahcing her destination, a backpacker walks with an average velocity of 1.29 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.59 m/s, due west, turns around, and hikes with an average velocity of 0.44 m/s, due east. How far east did she walk?
net distance divided by total time is 1.29m/s
Since time = distance/speed,
(6400-d)/(6400/2.59 + d/.44) = 1.29
d = 817m or .817km
check: she walked west for 6440/2.59 = 2486 s
she walked east for 817/.44 = 1857s
net distance from start: 5623m
total time hiking: 2486+1857 = 4343s
5623m/4343s = 1.29m/s
To determine how far east the backpacker walked, we need to find the total displacement in the east direction.
First, let's find the total displacement in the west direction. We know that the backpacker hiked for 6.44 km (6440 m) with an average velocity of 2.59 m/s in the west direction. We can use the formula:
Displacement = Velocity × Time
To find time, we can rearrange the formula:
Time = Displacement / Velocity
So, the time taken in the west direction is:
Time = 6440 m / 2.59 m/s = 2488.42 s
Now, the backpacker turns around and hikes for some distance with an average velocity of 0.44 m/s east. Let's assume the distance hiked in the east direction is d meters.
The time taken in the east direction can be calculated using the formula:
Time = Distance / Velocity
So, the time taken in the east direction is:
Time = d meters / 0.44 m/s = d / 0.44 s
Since the total time taken is the sum of the time taken in the west and east directions, we can write:
Total Time = Time in the West + Time in the East
2488.42 s = d / 0.44 s + d
Simplifying the equation:
2488.42 = (1.134 d + d)
2488.42 = 2.134 d
Solving for d:
d = 2488.42 / 2.134 ≈ 1166.094 m
Therefore, the backpacker walked approximately 1166.094 meters east.