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 find the sum of the individual displacements in the x-axis (east-west) and y-axis (north-south).
Let's assume that moving to the east is considered positive in the x-axis, and moving to the north is considered positive in the y-axis.
(a) To find the x-axis displacement:
The girl travels 2.00 blocks west initially and then travels 8.00 blocks east. So, the x-axis displacement is 8.00 - 2.00 = 6.00 blocks east.
(b) To find the y-axis displacement:
The girl travels 5.00 blocks north in the y-axis.
Now, we can use the x-axis and y-axis displacements to find the resultant displacement.
Using the Pythagorean theorem:
Resultant Displacement^2 = (x-axis displacement)^2 + (y-axis displacement)^2
Resultant Displacement^2 = (6.00)^2 + (5.00)^2
Resultant Displacement^2 = 36.00 + 25.00
Resultant Displacement^2 = 61.00
Taking the square root of both sides:
Resultant Displacement = √(61.00)
Resultant Displacement ≈ 7.81 blocks
To find the angle of the resultant displacement, we can use the inverse tangent function:
θ = tan^(-1)(y-axis displacement / x-axis displacement)
θ = tan^(-1)(5.00 / 6.00)
θ ≈ 40.95 degrees
Therefore, the girl's resultant displacement angle is approximately 40.95 degrees.
To find the resultant displacement, we need to calculate the net distance traveled in the north and west directions.
First, let's consider the north direction: The girl traveled 5 blocks north.
Next, let's consider the west direction: The girl traveled 2 blocks west.
Finally, let's consider the east direction: The girl traveled 8 blocks east.
Since the girl traveled in opposite directions (west and east), we need to subtract the eastward distance from the westward distance.
2 blocks west - 8 blocks east = -6 blocks east
So, the resultant displacement in the east direction is -6 blocks.
To determine the angle of the resultant displacement, we can use the trigonometric concept of tangent. The inverse tangent (tan⁻¹) will provide us with the angle.
tan⁻¹(opposite/adjacent) = tan⁻¹(5/6)
Using a calculator, we can find the angle:
tan⁻¹(5/6) ≈ 42.99 degrees
Therefore, the angle of the resultant displacement is approximately 43 degrees (rounded to two decimal places).