Hiker Displacement: Find Distance East

In summary, the backpacker walked with an average velocity of 1.34 m/s due west, completing a total distance of 6.44 km. She then turned around and walked with an average velocity of 0.447 m/s due east. To find the distance she walked due east, the equation \frac{6440}{2.68} + \frac{x}{0.447} = \frac{6440-x}{1.34} can be used, where x represents the distance due east."
  • #1
ayerski
4
0

Homework Statement


In reaching her destination, a backpacker walks with an average velocity of 1.34 m/s die west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.68 m/s, due west, turns around, and hikes with an average velocity of .447 m/s due east. How far east did she walk?


Homework Equations


velocity formula number 2


The Attempt at a Solution


Trying to use multiple variables to solve but need a push in the right direction
 
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  • #2
I'm not sure if this is correct, but the way I would do it is to compare the times taken for the first two parts of the journey with the time taken for the overall journey.

Using:

[tex]t=\frac{x}{v}[/tex]

gives the following equation which can easily be solved for x to find the distance due east.

[tex]\frac{6440}{2.68} + \frac{x}{0.447} = \frac{6440-x}{1.34}[/tex]

I hope that helps.

Ryan
 
  • #3
.

I would suggest approaching this problem using the formula for velocity, which is distance divided by time. We know that the average velocity for the entire hike is 1.34 m/s, and we can also calculate the total time for the hike by adding the time it took for the westward hike and the eastward hike. This would give us the total distance traveled, and we can then solve for the distance traveled east by subtracting the distance traveled west from the total distance. This would give us the distance traveled east as 5.73 km.
 

1. How is hiker displacement calculated?

Hiker displacement is calculated using the Pythagorean theorem, which states that the square of the hypotenuse (the longest side of a right triangle) is equal to the sum of the squares of the other two sides. In this case, the hiker's displacement is the hypotenuse, and the distance east and distance north are the other two sides.

2. What is the unit of measurement for hiker displacement?

The unit of measurement for hiker displacement is typically expressed in miles or kilometers, depending on the unit of measurement used for the distance east and distance north.

3. Can hiker displacement be negative?

Yes, hiker displacement can be negative. This occurs when the hiker is moving in a westward or southward direction, resulting in a negative distance east or distance north.

4. How can hiker displacement be used in navigation?

Hiker displacement can be used in navigation to determine the overall distance traveled in a specific direction. It can also be used to calculate the hiker's position relative to a starting point, and to determine the direction and distance to reach a destination.

5. Is hiker displacement affected by terrain or obstacles?

Yes, hiker displacement can be affected by terrain or obstacles. For example, if a hiker must navigate around a mountain or body of water, their displacement will be longer than if they were able to travel in a straight line. Additionally, rough terrain or steep inclines may slow down the hiker, resulting in a smaller displacement over a given amount of time.

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