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

[Alexandra Fabiello]

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.

 

[tnich]

You are almost there. You dropped a sign at this step, though.

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?

 

[Alexandra Fabiello]

t_east(0.495 m/s + 1.28 m/s) = t_east(1.775 m/s)

So 3155.856574 m /1.775 m/s = t_east = 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.

 

[tnich]

t_east(0.495 m/s + 1.28 m/s) = t_east(1.775 m/s)

So 3155.856574 m /1.775 m/s = t_east = 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