Suppose an airplane is flying 170 mph with a heading 25° east of south (295° measured counterclockwise from due east) when it encounters a 45 mph wind blowing steadily in a direction 15° north of east (15° measured counterclockwise from due east). Use 7 to represent the speed vector of the airplane and w to represent the speed vector of the wind. a. Start by drawing a head-to-tail configuration for 7 and w and the resultant vector v + w. b. Write both 7 and win component form. (Your answers should be in the form "< #, #>".) OV= OE= c. Write the resultant vector 7 + w in component form. v+w d. Now, write the resultant vector + w in polar form. (You do not need to enter a degree symbol in your answer.) v+w= e. Your answer to part (c) tells us that the plane is actually moving at counterclockwise of due east. mph in the direction

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Chapter1: Functions And Models
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### Vector Addition Problem

**Scenario:** 
Suppose an airplane is flying at 170 mph with a heading 25° east of south (295° measured counterclockwise from due east) when it encounters a 45 mph wind blowing steadily in a direction 15° north of east (15° measured counterclockwise from due east). Use **v** to represent the speed vector of the airplane and **w** to represent the speed vector of the wind.

**Tasks:**

a. **Draw a head-to-tail configuration for vectors** **v** and **w** and the resultant vector **v** + **w**.

b. **Write both** **v** and **w** **in component form.** *(Your answers should be in the form "<#, #>".)*

   - **v** = [Input required]
   - **w** = [Input required]

c. **Write the resultant vector** **v** + **w** **in component form.**

   - **v** + **w** = [Input required]

d. **Write the resultant vector** **v** + **w** **in polar form.** *(You do not need to enter a degree symbol in your answer.)*

   - **v** + **w** = [Input required]

e. **Your answer to part (c) tells us that the plane is actually moving at** [Input required] **mph in the direction** [Input required] **° counterclockwise of due east.**

---

### Graphs/Diagrams Explanation:

**Note:** Since this is a text-based platform, the specific graphical representation is not provided here. However, guidance is given to aid in manual drawing or conceptual understanding.

1. **Head-to-Tail Configuration:**
   - Start by drawing the vector **v** (airplane vector) with its tail at the origin. This vector is 170 mph at 25° east of south.
   - From the head of **v**, draw vector **w** (wind vector). This vector is 45 mph at 15° north of east.
   - The resultant vector **v** + **w** is drawn from the tail of **v** to the head of **w**.

2. **Component Form Calculation:**
   - For vector **v**:
     - The x-component is \( 170 \cos(295^\circ) \).
     - The y-component
Transcribed Image Text:### Vector Addition Problem **Scenario:** Suppose an airplane is flying at 170 mph with a heading 25° east of south (295° measured counterclockwise from due east) when it encounters a 45 mph wind blowing steadily in a direction 15° north of east (15° measured counterclockwise from due east). Use **v** to represent the speed vector of the airplane and **w** to represent the speed vector of the wind. **Tasks:** a. **Draw a head-to-tail configuration for vectors** **v** and **w** and the resultant vector **v** + **w**. b. **Write both** **v** and **w** **in component form.** *(Your answers should be in the form "<#, #>".)* - **v** = [Input required] - **w** = [Input required] c. **Write the resultant vector** **v** + **w** **in component form.** - **v** + **w** = [Input required] d. **Write the resultant vector** **v** + **w** **in polar form.** *(You do not need to enter a degree symbol in your answer.)* - **v** + **w** = [Input required] e. **Your answer to part (c) tells us that the plane is actually moving at** [Input required] **mph in the direction** [Input required] **° counterclockwise of due east.** --- ### Graphs/Diagrams Explanation: **Note:** Since this is a text-based platform, the specific graphical representation is not provided here. However, guidance is given to aid in manual drawing or conceptual understanding. 1. **Head-to-Tail Configuration:** - Start by drawing the vector **v** (airplane vector) with its tail at the origin. This vector is 170 mph at 25° east of south. - From the head of **v**, draw vector **w** (wind vector). This vector is 45 mph at 15° north of east. - The resultant vector **v** + **w** is drawn from the tail of **v** to the head of **w**. 2. **Component Form Calculation:** - For vector **v**: - The x-component is \( 170 \cos(295^\circ) \). - The y-component
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