A girl delivering newspapers travels 2 blocks
west, 10 blocks north, then 4 blocks east.
What is the magnitude of her resultant dis-
placement?
Answer in units of blocks.
077 (part 2 of 3) 10.0 points
Find the direction (measured from due east,
with counterclockwise positive) of her dis-
placement.
Answer in units of �
X = hor = 4 - 2 = 2 Blocks.
Y = ver. = 10 Blocks.
tanA = Y/X = 10 / 2 = 5,
A = 78.7 deg.
R = X/cosA = 2 /78.7 = 10.2 Blocks @
78.7Deg.
0 percent of correctness
To find the magnitude of the resultant displacement, you can use the Pythagorean theorem. Consider a right triangle where the two legs represent the distances traveled west and east (2 blocks and 4 blocks, respectively) and the hypotenuse represents the magnitude of the resultant displacement.
Using the Pythagorean theorem, you can calculate the magnitude by taking the square root of the sum of the squares of the two legs.
Magnitude of resultant displacement = √(2^2 + 4^2) = √(4 + 16) = √20 = 2√5
Therefore, the magnitude of her resultant displacement is 2√5 blocks.
Next, to find the direction of her displacement, we need to determine the angle measured counterclockwise from due east. To do this, we can use trigonometry.
Let's denote the angle of the displacement as θ. The adjacent side of the angle θ in the triangle would be the distance traveled west (2 blocks), and the hypotenuse is the magnitude of the resultant displacement we calculated earlier (2√5 blocks).
Using the cosine function, we can find the value of cosθ.
cosθ = adjacent/hypotenuse = 2/2√5 = 1/√5
To find the value of θ, we can take the inverse cosine (cos^(-1)) of 1/√5 using a calculator.
θ = cos^(-1)(1/√5) ≈ 63.43 degrees
Therefore, the direction of her displacement is approximately 63.43 degrees measured counterclockwise from due east.