A girl delivering newspapers covers her route by traveling 2.00 blocks west, 5.00 blocks north, and then 8.00 blocks east.
(a) What is her resultant displacement?
(only enter the angle of the resultant in the answer space below, not the distance)
enter it as a positive angle, between 0-360 degrees
To find the resultant displacement, we need to calculate the net distance traveled in both the horizontal and vertical directions.
First, let's calculate the net horizontal displacement. The girl travels 2 blocks to the west and then 8 blocks to the east. Since she travels in opposite directions, the net horizontal displacement is the difference between the distances traveled in each direction: 8 blocks - 2 blocks = 6 blocks to the east.
Next, let's calculate the net vertical displacement. The girl travels 5 blocks to the north and doesn't travel in the opposite direction in the vertical direction, so the net vertical displacement is 5 blocks to the north.
Now we have calculated the net horizontal and vertical displacements. To find the resultant displacement, we need to find the angle between the net displacement vector and the positive horizontal axis. We can use the tangent function to find this angle:
Angle = arctan(Vertical Displacement / Horizontal Displacement)
Plugging in the values, we get:
Angle = arctan(5 / 6)
Using a calculator, we find that Angle ≈ 39.8 degrees.
Therefore, the girl's resultant displacement angle is approximately 39.8 degrees.
To find the resultant displacement, we need to calculate the total distance traveled in the north and west directions and then determine the direction of the resultant vector.
The distance traveled in the north direction is 5.00 blocks, while the distance traveled in the west direction is 2.00 blocks. The eastward distance of 8.00 blocks cancels out the westward distance.
Since the net displacement is vertical (north), we can use the inverse tangent function to find the angle:
angle = arctan(north distance / west distance)
angle = arctan(5.00 / 2.00)
Using a calculator, we find that arctan(5.00 / 2.00) ≈ 68.2 degrees.
Therefore, the resultant displacement is approximately 68.2 degrees.
a. D = -2 + 5i + 8 = 6 + 5i.
D2 = 6^2 + 5^2 = 61
D = 7.81 Blocks.
b. ta A = Y/X = 5/6 = 0.83333
A = 39.8o