You walk for 6.44 km with at a constant velocity of 2.54 m/s due west, turn around, and then walk with an average velocity of 0.480 m/s due east. From your starting point to your destination, your overall average velocity is 1.29 m/s due west. During the trip, how far east did you walk?
To find out how far east you walked during the trip, we can use the concept of average velocity.
First, let's calculate the time it took to walk the first leg of the trip, which is 6.44 km at a velocity of 2.54 m/s due west.
Time = Distance / Velocity = 6.44 km / 2.54 m/s
To calculate time, we need to convert kilometers to meters:
6.44 km = 6.44 x 1000 m = 6440 m
So,
Time = 6440 m / 2.54 m/s
Next, let's calculate the distance you walked during the second leg of the trip, which is at an average velocity of 0.480 m/s due east. We'll call this distance 'd'.
Average Velocity = Total Distance / Total Time
1.29 m/s = (6.44 km + d) / (6440 m / 2.54 m/s)
Now, let's solve for 'd' to find out how far east you walked:
1.29 m/s = (6.44 km + d) / (6440 m / 2.54 m/s)
Multiplying both sides of the equation by (6440 m / 2.54 m/s):
(1.29 m/s) * (6440 m / 2.54 m/s) = 6.44 km + d
Now, let's solve for 'd' by subtracting 6.44 km from both sides:
(1.29 m/s) * (6440 m / 2.54 m/s) - 6.44 km = d
Calculating this expression, we find:
4107.086614 km - 6.44 km = d
So, the distance you walked east during the trip is approximately 4100.646614 km.