The inquiry is unfinished. Below is the complete question.
The attached map depicts Olivia's journey to the coffee shop. She rides her bike south for 0.9mi to Broadway after starting at Loomis. Next, she turns east onto Broadway, traveling 0.8mi until the road curves, and then she proceeds another 1.4mi to reach the shop.
What is the total displacement magnitude of her journey?
What direction does the total displacement of her journey take?
Response: Magnitude = 2.6mi
Direction: 54.65° east
Clarification: Displacement refers to the change in position of a moving entity.
There are various methods to calculate total displacement. In this scenario, the method of Perpendicular Components of a Vector will be applied.
This method calculates total displacement as follows:
represents the x-component of the total displacement, which is the total of all individual x-components;
stands for the y-component of the total displacement, calculated by summing all individual y-components;
θ signifies the angle of the resultant displacement;
In Olivia's case, there is no x-component for the first leg, and for the last segment, the biking path acts as the hypotenuse of a right triangle. Therefore, the x-component of that triangle is:
x = 0.7
Consequently,
= 0 + 0.8 + 0.7
= 1.5
Regarding the y-component, there’s no y-component in the second portion of Olivia's ride, and in the last segment:
y = 1.21
Thus,
= 0.9 + 0 + 1.21
= 2.11
The total displacement is
2.6
The magnitude of Olivia's total displacement is 2.6mi
Connecting the starting and ending points on the map forms a vector directed eastward, at an angle of:
θ = 54.65°
The direction of the total displacement is 54.65° East.
, where G indicates the gravitational constant. If the satellite is positioned directly on the planet's surface, the distance between the two masses becomes r, and the gravitational force is represented as 
. The answer is: 
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