Finding distance east given west dist., velocities, and average velocity

In summary, by converting the given values and using algebraic equations, we can calculate that the total time is 1777.947366 seconds going east and the distance walked east is 880.083946 meters, rounded to 3 significant figures.
  • #1
Alexandra Fabiello
42
1
Homework Statement
You walk for 6.44 km with at a constant velocity of 2.51 m/s due west, turn around, and then walk with an average velocity of 0.495 m/s due east. From your starting point to your destination, your overall average velocity is 1.28 m/s due west. During the trip, how far east did you walk?
Hint: There are a number of issues to think about in this problem: The average velocity is the displacement, from initial point to final point, divided by the total time. Set up an equation for the average velocity in terms of the initial and final position and the total time. You can find the time it takes to walk west from the distance and velocity. You will need to substitute expressions for the velocity of each segment into the expression for the average velocity. Watch signs of positions and velocities, and unit conversions.
Relevant Equations
v = change in displacement/change in time
distance = velocity * time
av * total time = (west velocity * west time) - (east velocity * east time)
6.44 km * 1000 = 6440 m/2.51 m/s = 2565.737052 s = west time

av = (6440 m + - east distance)/(2565.737052 s + east time)

2565.737052 s + east time = total time

1.28 m/s * total time = (6440 m) - (0.495 m/s * east time)

1.28 m/s * (2565.737052 s + east time) = (6440 m) - (0.495 m/s * east time)

3284.143426 m +1.28 m/s(east time) - 6440 m = - (0.495 m/s * east time)

3155.856574 m = (0.495 m/s * east time) - 1.28 m/s(east time)

And now I'm stuck because it seems multiplying out will end up with lots of 'east time's and I'm not sure how to convert properly.
 
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  • #2
You are almost there. You dropped a sign at this step, though.
Alexandra Fabiello said:
3155.856574 m = (0.495 m/s * east time) - 1.28 m/s(east time)
If you had
$$0.495t_{east}+1.28t_{east}$$
how would you simplify it?
 
  • #3
teast(0.495 m/s + 1.28 m/s) = teast(1.775 m/s)

So 3155.856574 m /1.775 m/s = teast = 1777.947366 s going east

1777.947366 s * 0.495 m/s = 880.083946 m walked east = 8.80*102 m walked east rounded to 3 significant figures.

Right?

Thank you so much. Missed the obvious, but that's why I come here sometimes. Thanks again.
 
  • #4
Alexandra Fabiello said:
teast(0.495 m/s + 1.28 m/s) = teast(1.775 m/s)

So 3155.856574 m /1.775 m/s = teast = 1777.947366 s going east

1777.947366 s * 0.495 m/s = 880.083946 m walked east = 8.80*102 m walked east rounded to 3 significant figures.

Right?

Thank you so much. Missed the obvious, but that's why I come here sometimes. Thanks again.
Yes
 

FAQ: Finding distance east given west dist., velocities, and average velocity

1) What is the formula for finding distance east given west distance, velocities, and average velocity?

The formula for finding distance east is: Distance East = (West Distance / Average Velocity) * Velocity East

2) How do you calculate average velocity?

Average velocity is calculated by dividing the total displacement by the total time taken.

3) Can you provide an example of finding distance east using this formula?

For example, if the west distance is 50 miles, the average velocity is 25 miles per hour, and the velocity east is 20 miles per hour, then the distance east would be (50/25) * 20 = 40 miles.

4) Is this formula applicable to all types of motion?

Yes, this formula can be used for any type of motion where there is a displacement in both the east and west directions, and there is a constant average velocity.

5) How can this formula be used in real-world situations?

This formula can be used in various real-world situations, such as calculating the distance a ship has traveled east from its starting point given its westward distance, speeds, and average velocity. It can also be used in navigation and transportation to determine the distance and time needed to reach a destination.

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