In reaching her destination, a backpacker walks with an average velocity of 1.21

[mytalkingbird]

Homework Statement

In reaching her destination, a backpacker walks with an average velocity of 1.21 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.52 m/s, due west, turns around, and hikes with an average velocity of 0.435 m/s, due east. How far east did she walk? in km? ______km

Homework Equations

The Attempt at a Solution

 

[tvavanasd]

Attempt?

 

[mytalkingbird]

Attempt?

6.44(1000)=(6440m)/(1.21m/s)=(5322.31405seconds)/2.52m/s=2112.029

(6440-d) + ((6440-d)/.435)) = d/1.21

i'm lost. i don't know what to do next.

 

[tvavanasd]

Start by listing all variables that you know. Solve symbolically; it will be too confusing otherwise.
You already know v = x / t and t = x / v
Use and manipulate:
V3 = X3 / T3 (this is average overall)
T3 = T1 + T2
X3 = X1 + X2
You will also need V1 = X1 / T1 and V2 = X2 / T2 (manipulate as necessary).
Solve for Xtotal, then assume that west is positive (east is -ve) and substitute X1 = 6440 m, V1 = 2.52m/s, V3 = 1.21 m/s and V2 = -0.435 m/s

Note that X3 will be her displacement from start to finish, not the total distance that she walked.

 

[rwisz]

I would first like to clarify that velocity is a vector quantity, meaning it has both magnitude (speed) and direction. In this scenario, the backpacker's average velocity of 1.21 m/s tells us that she traveled at a constant speed of 1.21 m/s in a due west direction.

To answer the question, we can use the equation v = d/t, where v is the velocity, d is the distance traveled, and t is the time it took to travel that distance. We are given the average velocity and the distance traveled in two separate segments, so we can calculate the total time it took the backpacker to reach her destination.

First, we can find the total distance traveled by adding the two distances given: 6.44 km + d = total distance.

Next, we can use the average velocity equation for the first segment: 2.52 m/s = (6.44 km)/t. Solving for t, we get t = 6.44 km / 2.52 m/s = 2.56 x 10^3 s.

Using the same equation for the second segment, we can find the time it took to travel d km: 0.435 m/s = d/t. Solving for t, we get t = d / 0.435 m/s = 2.56 x 10^3 s.

Since the total time is the same for both segments, we can set the two equations equal to each other and solve for d:

6.44 km / 2.52 m/s = d / 0.435 m/s

d = (6.44 km / 2.52 m/s) x 0.435 m/s = 1.11 km

Therefore, the backpacker walked 1.11 km east during the second segment of her journey.

In summary, the backpacker walked a total distance of 7.55 km (6.44 km + 1.11 km) and 1.11 km of that distance was in an eastward direction.