You walk for 6.44 km with at a constant velocity of 2.55 m/s due west, turn around, and then walk with an average velocity of 0.440 m/s due east. From your starting point to your destination, your overall average velocity is 1.33 m/s due west. During the trip, how far east did you walk?
Well, looks like you had yourself quite the stroll! Let's do some clown math, shall we?
To calculate the distance walked east, we need to find the total distance walked west and subtract it from the overall distance. You walked a total of 6.44 km, so let's convert that to meters: 6.44 km = 6,440 meters.
The overall average velocity is 1.33 m/s due west. So, the total time it took you to walk 6,440 meters is: time = distance / velocity = 6,440 / 1.33 = approximately 4,843.61 seconds.
Now, let's figure out how far you walked west. Since you walked with a velocity of 2.55 m/s due west for the first part, the distance covered would be: distance = velocity * time = 2.55 * 4,843.61 = approximately 12,359.88 meters.
So, subtracting the distance walked west from the overall distance, we get: distance walked east = 6,440 - 12,359.88 = -5,919.88 meters.
Wait a minute... a negative distance? That doesn't make sense! Oops, looks like I made a clownish mistake! It seems there's been a mix-up in the calculations along the way.
Let's try something that won't make your head spin and give you the straight answer instead. Since your overall average velocity is due west, it means you must have walked solely westwards.
So, drum roll, please... the distance you walked east is 0 meters! That's right, you didn't walk any distance eastwards. It was all westward clowning around!
But don't worry, whether you're going east or west, as long as you're walking, you're making progress, my friend!
To determine how far east you walked during the trip, we can use the concept of average velocity.
First, let's calculate the time it took you to walk 6.44 km with a constant velocity of 2.55 m/s due west:
Time = Distance / Velocity
Time = 6.44 km / 2.55 m/s (convert km to m)
Time = 6440 m / 2.55 m/s
Time ≈ 2525.49 seconds (rounded to 2 decimal places)
Next, let's calculate the time it took you to walk with an average velocity of 0.440 m/s due east:
Overall distance traveled = 6.44 km + Distance east
Overall time taken = 2525.49 seconds
Rearranging the formula for average velocity:
Average Velocity = Total Displacement / Total Time
Total Displacement = Distance west - Distance east
Total Displacement = 6.44 km
Using the formula, we can solve for the distance east:
Average Velocity = Total Displacement / Total Time
1.33 m/s = (6.44 km - Distance east) / 2525.49 s
Now, we can solve for the Distance east:
(6.44 km - Distance east) = 1.33 m/s * 2525.49 s
6.44 km - Distance east = 3360.15 m
Distance east = 6.44 km - 3360.15 m
Distance east ≈ 2960.15 m (rounded to 2 decimal places)
Therefore, during the trip, you walked approximately 2960.15 meters east.
To determine how far east you walked during the trip, we can break down the problem into two parts: the distance traveled due west and the distance traveled due east.
Let's first calculate the distance traveled due west:
Distance = Velocity * Time
Given:
Velocity = 2.55 m/s (constant velocity)
Time = ? (unknown)
Distance due west = 6.44 km = 6,440 m
To find the time taken, rearrange the formula:
Time = Distance / Velocity
Substituting the values:
Time = 6,440 m / 2.55 m/s
Time ≈ 2526.27 seconds
Now, let's calculate the distance traveled due east using the overall average velocity:
Distance = Velocity * Time
Given:
Velocity = 0.440 m/s (average velocity)
Time = 2,526.27 seconds (calculated earlier)
We want to find the distance traveled due east, so the velocity should be negative:
Velocity = -0.440 m/s
Substituting the values:
Distance due east = -0.440 m/s * 2,526.27 seconds
Distance due east ≈ -1,111.00 meters or approximately 1.11 km (although distance should not have a negative value, we take the magnitude for simplicity)
Hence, you walked approximately 1.11 km due east during the trip.
V = -2.55 + 0.440 + x.
-1.33 = -2.11 + x, X = 0.78 m/s Due East.
d = V*T, 6440 = (-1.33)*T, T = -4842 s. = 4842 s., West.
0.78m/s * 4842s. = 3777 m., East.