A girl delivering newspapers covers her route by traveling 10.00 blocks west, 4.00 blocks north, and then 5.00 blocks east.
a.) what is her resultant displacement?
b.) what is the total distance she travels?
To find the resultant displacement, we need to consider both the magnitude (distance) and direction of each leg of the journey. We can use the concept of vectors to simplify the calculations.
a.) To find the resultant displacement, we can treat each leg of the journey as a vector and then add them together. Let's break down the journey into three vectors:
1. First leg: 10.00 blocks west.
We can represent this vector as -10.00 blocks east (since west is the opposite direction of east).
The vector can be written as -10.00i, where "i" represents the horizontal axis.
2. Second leg: 4.00 blocks north.
This vector can be written as 4.00j, where "j" represents the vertical axis.
3. Third leg: 5.00 blocks east.
We can represent this vector as 5.00i.
Now, let's add the three vectors together:
Resultant displacement = -10.00i + 4.00j + 5.00i
Since i represents the horizontal axis and j represents the vertical axis, we can treat them separately.
Horizontal component = -10.00i + 5.00i = -5.00i
Vertical component = 4.00j
Therefore, the resultant displacement vector is -5.00i + 4.00j. This means that the girl ends up 5.00 blocks west and 4.00 blocks north from her starting point.
b.) To find the total distance traveled, we can sum up the magnitudes (distances) of each leg of the journey.
The distance traveled on the first leg (10.00 blocks west) is 10.00 blocks.
The distance traveled on the second leg (4.00 blocks north) is 4.00 blocks.
The distance traveled on the third leg (5.00 blocks east) is also 5.00 blocks.
Total distance traveled = 10.00 + 4.00 + 5.00 = 19.00 blocks.
Hence, the girl's resultant displacement is -5.00i + 4.00j, and the total distance she traveled is 19.00 blocks.
d=sqrt( 4²+5²)=6.4
s=10+4+5=19