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Please answer parts A and B. Please show all work and circle your answer! Thank you in advanced!
![Here is the transcription and explanation for the given text and problem:
---
**Equations:**
\[
v_{fy} = v_{iy} + a_y \cdot t
\]
\[
y_f = y_i + v_{iy} \cdot t + \frac{1}{2} a_y \cdot t^2
\]
\[
v_{fy}^2 = v_{iy}^2 + 2a_y \cdot (y_f - y_i)
\]
\[
y_f - y_i = \frac{1}{2} (v_{iy} + v_{fy}) \cdot t
\]
\[
\Delta y \equiv y_f - y_i
\]
**1) Vectors**
\[
\vec{A} = 2 \cdot \hat{i} - 3 \cdot \hat{j} = (2, -3)
\]
\[
\vec{B} = -4 \cdot \hat{i} + 5 \cdot \hat{j} = (-4, 5)
\]
**a)** Given the vectors above, find the vector \(\vec{C} = \vec{A} - \vec{B}\) and express it in either one of the two ways shown above (either using the unit vectors or as an ordered pair of coordinates in brackets separated by a comma).
\[
\vec{C} = 6 \cdot \hat{i} - 8 \cdot \hat{j} = (6, -8)
\]
**b)** Find the magnitude \( C \) of the vector you found in part (a).
\[
|\vec{C}| = \sqrt{6^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ units}
\]
---
The problem provides equations related to motion and vectors and then focuses on computing the result of a vector subtraction followed by calculating the magnitude of that resulting vector.](https://content.bartleby.com/qna-images/question/185a2ffd-98a0-4e7f-8b74-4ff84feecadd/6997738c-2f43-4f85-af67-9d106550fafa/byc1hb_processed.jpeg)
Transcribed Image Text:Here is the transcription and explanation for the given text and problem:
---
**Equations:**
\[
v_{fy} = v_{iy} + a_y \cdot t
\]
\[
y_f = y_i + v_{iy} \cdot t + \frac{1}{2} a_y \cdot t^2
\]
\[
v_{fy}^2 = v_{iy}^2 + 2a_y \cdot (y_f - y_i)
\]
\[
y_f - y_i = \frac{1}{2} (v_{iy} + v_{fy}) \cdot t
\]
\[
\Delta y \equiv y_f - y_i
\]
**1) Vectors**
\[
\vec{A} = 2 \cdot \hat{i} - 3 \cdot \hat{j} = (2, -3)
\]
\[
\vec{B} = -4 \cdot \hat{i} + 5 \cdot \hat{j} = (-4, 5)
\]
**a)** Given the vectors above, find the vector \(\vec{C} = \vec{A} - \vec{B}\) and express it in either one of the two ways shown above (either using the unit vectors or as an ordered pair of coordinates in brackets separated by a comma).
\[
\vec{C} = 6 \cdot \hat{i} - 8 \cdot \hat{j} = (6, -8)
\]
**b)** Find the magnitude \( C \) of the vector you found in part (a).
\[
|\vec{C}| = \sqrt{6^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ units}
\]
---
The problem provides equations related to motion and vectors and then focuses on computing the result of a vector subtraction followed by calculating the magnitude of that resulting vector.
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