Answer
To sketch the graph of the airplane's height over time:
1. **Ascent (0 to 15 minutes):** Draw a straight line upward from (0,0) to (15, Cruising Altitude).
2. **Cruising (15 to 105 minutes):** Draw a horizontal line from (15, Cruising Altitude) to (105, Cruising Altitude).
3. **Descent (105 to 125 minutes):** Draw a straight line downward from (105, Cruising Altitude) to (125, 0).
This will show the airplane ascending, maintaining altitude, and then descending over the 125-minute flight.
Solution
To sketch the graph of the **height of the plane over time**, let's break down the flight into its three distinct phases:
1. **Ascent (0 to 15 minutes):**
- **Description:** The airplane takes off and ascends smoothly to its cruising altitude.
- **Graph Representation:** A **linear upward slope** from the origin (0 minutes) reaching the cruising altitude at 15 minutes.
2. **Cruising (15 to 105 minutes):**
- **Description:** The airplane maintains a constant cruising altitude.
- **Graph Representation:** A **horizontal line** indicating constant height from 15 minutes to 105 minutes.
3. **Descent (105 to 125 minutes):**
- **Description:** The airplane descends smoothly back to ground level for landing.
- **Graph Representation:** A **linear downward slope** from cruising altitude at 105 minutes down to ground level at 125 minutes.
### Visual Representation
While I can't provide an actual sketch here, here's a textual representation to help you visualize the graph:
```
Height
↑
| ____________
| | |
| | |
| | |
| | |
| | |
|_______________| |_______________ Time
0 15 105 125 (minutes)
```
- **From 0 to 15 minutes:** The line slopes upward, representing the ascent.
- **From 15 to 105 minutes:** The line is flat, representing the cruising phase with constant altitude.
- **From 105 to 125 minutes:** The line slopes downward, representing the descent.
### Key Points to Plot
1. **Start Point:** (0 minutes, 0 altitude)
2. **End of Ascent:** (15 minutes, Cruising Altitude)
3. **End of Cruising:** (105 minutes, Cruising Altitude)
4. **End of Descent:** (125 minutes, 0 altitude)
### Steps to Sketch the Graph
1. **Draw the Axes:**
- **Horizontal Axis (X-axis):** Label as "Time (minutes)" ranging from 0 to 125.
- **Vertical Axis (Y-axis):** Label as "Height" with appropriate units (e.g., meters or feet).
2. **Plot the Ascent:**
- Draw a straight line from (0, 0) to (15, Cruising Altitude).
3. **Plot the Cruising Phase:**
- Draw a horizontal line from (15, Cruising Altitude) to (105, Cruising Altitude).
4. **Plot the Descent:**
- Draw a straight line from (105, Cruising Altitude) to (125, 0).
5. **Label the Phases:**
- Optionally, annotate each phase (Ascent, Cruising, Descent) on the graph for clarity.
### Example with Arbitrary Cruising Altitude
Assuming the cruising altitude is **30,000 feet**, here's how the points would look:
- **Start Point:** (0, 0)
- **End of Ascent:** (15, 30,000)
- **End of Cruising:** (105, 30,000)
- **End of Descent:** (125, 0)
Using these points, you can accurately sketch the graph representing the airplane's height over the 125-minute flight duration.
Reviewed and approved by the UpStudy tutoring team
Explain
Simplify this solution
