A jet is flying with uniform motion at 9.3 x 102 m/s [S], the magnitude of which is approximately Mach 2.7. At the time zero, it passes a mountain top, which is used as the reference point for this question. a) Construct a table showig the plane's position relative to the mountain top at the end of each second for a 12 s period.
To construct a table showing the plane's position relative to the mountain top at the end of each second for a 12-second period, we need to use the plane's uniform motion and the initial position of the mountain top as the reference point.
We know that the plane is flying at a speed of 9.3 x 10^2 m/s [S]. This means it is traveling towards the south. The magnitude of the plane's speed is approximately Mach 2.7, which is a measure of the speed of sound in air.
Let's construct the table step by step:
First, let's establish the initial position of the plane relative to the mountain top. Since the plane passes the mountain top at time zero, we can assume the initial position to be zero for simplicity.
Table:
| Time (s) | Position relative to mountain top (m) |
|---------|---------------------------------|
| 0 | 0 |
Next, let's calculate the position of the plane at the end of each second for a 12-second period. The plane's speed is 9.3 x 10^2 m/s [S]. Since the plane is flying at a constant velocity, we can simply add the speed multiplied by the time elapsed to the previous position in each second.
Formula: Position = Initial position + (Speed x Time)
Table:
| Time (s) | Position relative to mountain top (m) |
|---------|---------------------------------|
| 0 | 0 |
| 1 | 9.3 x 10^2 [S] |
| 2 | (9.3 x 10^2 [S]) x 2 |
| 3 | (9.3 x 10^2 [S]) x 3 |
| 4 | (9.3 x 10^2 [S]) x 4 |
| 5 | (9.3 x 10^2 [S]) x 5 |
| 6 | (9.3 x 10^2 [S]) x 6 |
| 7 | (9.3 x 10^2 [S]) x 7 |
| 8 | (9.3 x 10^2 [S]) x 8 |
| 9 | (9.3 x 10^2 [S]) x 9 |
| 10 | (9.3 x 10^2 [S]) x 10 |
| 11 | (9.3 x 10^2 [S]) x 11 |
| 12 | (9.3 x 10^2 [S]) x 12 |
Simplifying the calculations, the table becomes:
Table:
| Time (s) | Position relative to mountain top (m) |
|---------|---------------------------------|
| 0 | 0 |
| 1 | 9.3 x 10^2 [S] |
| 2 | 1.86 x 10^3 [S] |
| 3 | 2.79 x 10^3 [S] |
| 4 | 3.72 x 10^3 [S] |
| 5 | 4.65 x 10^3 [S] |
| 6 | 5.58 x 10^3 [S] |
| 7 | 6.51 x 10^3 [S] |
| 8 | 7.44 x 10^3 [S] |
| 9 | 8.37 x 10^3 [S] |
| 10 | 9.3 x 10^3 [S] |
| 11 | 1.08 x 10^4 [S] |
| 12 | 1.17 x 10^4 [S] |
This table shows the plane's position relative to the mountain top at the end of each second for a 12-second period. The plane starts at zero position and moves uniformly towards the south, increasing its position by 9.3 x 10^2 meters per second.