Q: a model rocket was launched and measurements of its height and horizontal distances from the launched pad were taken as shown in the table
horizontal distance from the launch pad/m : 0,1,2,3,4,5,6,7,8,9,10,11.
vertical distance from the launch pad/m: 0,4,8,11,13,14.2,15,15.5,15,13,10,0
Q:If rocket had been 10 m above the ground when its horizontal distance from the launchpad was 2m ,wheredo you think rocket would have landed???
PLEASE HELP
To answer this question, let's analyze the data provided in the table. The table shows the vertical distance of the rocket from the launch pad at various horizontal distances.
We can observe that when the horizontal distance is 0, the vertical distance is also 0. This indicates that the rocket was at ground level when it was launched.
Now, we need to find the point where the rocket was 10 meters above the ground (vertical distance) when its horizontal distance from the launch pad was 2 meters. We can use linear interpolation to estimate this point.
First, let's identify the two data points closest to the desired horizontal distance of 2 meters. From the table, we find that the closest data points are:
- When the horizontal distance is 1 meter, the vertical distance is 4 meters.
- When the horizontal distance is 3 meters, the vertical distance is 11 meters.
Using these two data points, we can calculate the slope of the line connecting them. The slope is given by the formula:
slope = (change in vertical distance) / (change in horizontal distance)
slope = (11 - 4) / (3 - 1) = 7 / 2 = 3.5
Now, using the slope and the vertical distance at the first data point (4 meters), we can determine the vertical distance when the horizontal distance is 2 meters. This is given by the formula:
(vertical distance) = (slope) * (horizontal distance - 1) + (vertical distance at 1 meter)
(vertical distance) = 3.5 * (2 - 1) + 4 = 3.5 + 4 = 7.5
Therefore, we estimate that the rocket would have landed at a vertical distance of 7.5 meters when its horizontal distance from the launch pad was 2 meters.
Please note that this estimation is based on linear interpolation using the given data points. It assumes a linear relationship between the rocket's vertical and horizontal distances, which may not be entirely accurate. Real-world factors like wind resistance and trajectory can affect the actual landing position of the rocket.