**Problem Description: Airplane Speed and Wind Effects** An airplane maintains a speed of 579 km/h relative to the air it is flying through as it makes a trip to a city 696 km away to the north. (Assume north is the positive y-direction and east is the positive x-direction.) **Questions:** (a) What time interval is required for the trip if the plane flies through a headwind blowing at 37.5 km/h toward the south? [Answer box for part (a)] h (b) What time interval is required if there is a tailwind with the same speed? [Answer box for part (b)] h (c) What time interval is required if there is a crosswind blowing at 37.5 km/h to the east relative to the ground? [Answer box for part (c)] h **Explanation of Concepts:** - **Headwind and Tailwind:** Headwinds slow down the airplane by reducing its effective speed relative to the ground, whereas tailwinds accelerate the airplane by increasing its effective speed. - **Crosswind:** A crosswind blows perpendicular to the direction of travel, affecting the trajectory but not the speed along the direct path to the destination. Use the formula for time: \( \text{Time} = \frac{\text{Distance}}{\text{Effective Speed}} \) to solve for each condition listed above.
**Problem Description: Airplane Speed and Wind Effects** An airplane maintains a speed of 579 km/h relative to the air it is flying through as it makes a trip to a city 696 km away to the north. (Assume north is the positive y-direction and east is the positive x-direction.) **Questions:** (a) What time interval is required for the trip if the plane flies through a headwind blowing at 37.5 km/h toward the south? [Answer box for part (a)] h (b) What time interval is required if there is a tailwind with the same speed? [Answer box for part (b)] h (c) What time interval is required if there is a crosswind blowing at 37.5 km/h to the east relative to the ground? [Answer box for part (c)] h **Explanation of Concepts:** - **Headwind and Tailwind:** Headwinds slow down the airplane by reducing its effective speed relative to the ground, whereas tailwinds accelerate the airplane by increasing its effective speed. - **Crosswind:** A crosswind blows perpendicular to the direction of travel, affecting the trajectory but not the speed along the direct path to the destination. Use the formula for time: \( \text{Time} = \frac{\text{Distance}}{\text{Effective Speed}} \) to solve for each condition listed above.
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![**Problem Description: Airplane Speed and Wind Effects**
An airplane maintains a speed of 579 km/h relative to the air it is flying through as it makes a trip to a city 696 km away to the north. (Assume north is the positive y-direction and east is the positive x-direction.)
**Questions:**
(a) What time interval is required for the trip if the plane flies through a headwind blowing at 37.5 km/h toward the south?
[Answer box for part (a)] h
(b) What time interval is required if there is a tailwind with the same speed?
[Answer box for part (b)] h
(c) What time interval is required if there is a crosswind blowing at 37.5 km/h to the east relative to the ground?
[Answer box for part (c)] h
**Explanation of Concepts:**
- **Headwind and Tailwind:** Headwinds slow down the airplane by reducing its effective speed relative to the ground, whereas tailwinds accelerate the airplane by increasing its effective speed.
- **Crosswind:** A crosswind blows perpendicular to the direction of travel, affecting the trajectory but not the speed along the direct path to the destination.
Use the formula for time: \( \text{Time} = \frac{\text{Distance}}{\text{Effective Speed}} \) to solve for each condition listed above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d158991-3671-4459-aef6-bd0615668acc%2Ffd0d41e0-e639-47be-a097-b10865d14d75%2Fktng2hb_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description: Airplane Speed and Wind Effects**
An airplane maintains a speed of 579 km/h relative to the air it is flying through as it makes a trip to a city 696 km away to the north. (Assume north is the positive y-direction and east is the positive x-direction.)
**Questions:**
(a) What time interval is required for the trip if the plane flies through a headwind blowing at 37.5 km/h toward the south?
[Answer box for part (a)] h
(b) What time interval is required if there is a tailwind with the same speed?
[Answer box for part (b)] h
(c) What time interval is required if there is a crosswind blowing at 37.5 km/h to the east relative to the ground?
[Answer box for part (c)] h
**Explanation of Concepts:**
- **Headwind and Tailwind:** Headwinds slow down the airplane by reducing its effective speed relative to the ground, whereas tailwinds accelerate the airplane by increasing its effective speed.
- **Crosswind:** A crosswind blows perpendicular to the direction of travel, affecting the trajectory but not the speed along the direct path to the destination.
Use the formula for time: \( \text{Time} = \frac{\text{Distance}}{\text{Effective Speed}} \) to solve for each condition listed above.
Expert Solution
Step 1
Given,
Speed of airplane along the north.
Distance covered by airplane in north direction.
North is positive y-axis and east is positive x-axis.
Speed of headwind along the south.
Speed of tailwind along the north.
Speed of crosswind along the east.
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