Question
What is the solution to the math problem involving an airplane heading at a bearing of N23°E at a speed of 700 km/hr?
Answers
GPT-4o mini
To solve a problem involving an airplane heading at a bearing of N23°E at a speed of 700 km/hr, we can break down the problem into components.
1. **Understand the Bearing**: The bearing N23°E means the airplane is heading 23 degrees east of due north.
2. **Convert the Bearing to Cartesian Components**:
- The angle from the positive x-axis (east) is 90° - 23° = 67°.
- Thus, we can calculate the northward (y-axis) and eastward (x-axis) components of the velocity.
3. **Calculate the Velocity Components**:
- The northward component \( V_y \) is given by:
\[
V_y = 700 \cdot \cos(23°)
\]
- The eastward component \( V_x \) is given by:
\[
V_x = 700 \cdot \sin(23°)
\]
4. **Find the Components**:
- Using approximate values, we find:
\(\cos(23°) \approx 0.9205\) and \(\sin(23°) \approx 0.3907\).
- Therefore:
\[
V_y \approx 700 \cdot 0.9205 \approx 644.35 \text{ km/hr}
\]
\[
V_x \approx 700 \cdot 0.3907 \approx 273.49 \text{ km/hr}
\]
5. **Final Result**:
- The airplane's velocity components are approximately:
- Northward component: **644.35 km/hr**
- Eastward component: **273.49 km/hr**
This provides the airplane's direction and speed in terms of its components along the north and east axes. If you need further information or calculations, please specify!
1. **Understand the Bearing**: The bearing N23°E means the airplane is heading 23 degrees east of due north.
2. **Convert the Bearing to Cartesian Components**:
- The angle from the positive x-axis (east) is 90° - 23° = 67°.
- Thus, we can calculate the northward (y-axis) and eastward (x-axis) components of the velocity.
3. **Calculate the Velocity Components**:
- The northward component \( V_y \) is given by:
\[
V_y = 700 \cdot \cos(23°)
\]
- The eastward component \( V_x \) is given by:
\[
V_x = 700 \cdot \sin(23°)
\]
4. **Find the Components**:
- Using approximate values, we find:
\(\cos(23°) \approx 0.9205\) and \(\sin(23°) \approx 0.3907\).
- Therefore:
\[
V_y \approx 700 \cdot 0.9205 \approx 644.35 \text{ km/hr}
\]
\[
V_x \approx 700 \cdot 0.3907 \approx 273.49 \text{ km/hr}
\]
5. **Final Result**:
- The airplane's velocity components are approximately:
- Northward component: **644.35 km/hr**
- Eastward component: **273.49 km/hr**
This provides the airplane's direction and speed in terms of its components along the north and east axes. If you need further information or calculations, please specify!