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
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
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F357dca67-e61c-42cc-8457-777054423446%2Fc1926efc-1965-4a40-b86c-526665b20960%2Fetx667_processed.jpeg&w=3840&q=75)
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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