hows a map of Olivia's trip to a coffee shop. She gets on her bike at Loomis and then rides south 0.9mi to Broadway. She turns e

Question

nikitadnepr

3 months ago

10

hows a map of Olivia's trip to a coffee shop. She gets on her bike at Loomis and then rides south 0.9mi to Broadway. She turns e

ast onto Broadway, rides 0.8 mi to where Broadway turns, and then continues another 1.4mi to the shop.

Physics

1 answer:

Softa [3K] · Answer 1 · 2026-02-17T05:39:07+03:00

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:

$\Delta d_{t}=\sqrt{(\Delta d_{x})^{2}+(\Delta d_{y})^{2}}$

$\theta=tan^{-1}(\frac{\Delta d_{y}}{\Delta d_{x}})$

$\Delta d_{x}$ represents the x-component of the total displacement, which is the total of all individual x-components;

$\Delta d_{y}$ 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:

$sin30=\frac{x}{1.4}$