Question
It rises 18m every 3 s. After 5s, the drone is at a height of 40m, What is the rate of change?
Answers
GPT-4o mini
To find the rate of change of the drone's height, we first need to determine its vertical speed, which can be calculated based on the information provided.
The drone rises 18 meters every 3 seconds. We can calculate the rate of change (or speed) as follows:
\[
\text{Rate of change} = \frac{\text{Height increase}}{\text{Time interval}} = \frac{18 \text{ m}}{3 \text{ s}} = 6 \text{ m/s}
\]
Now, we also want to verify that the drone being at a height of 40 meters after 5 seconds fits within this rate of change.
1. Calculate the total height the drone would have after 5 seconds at a rate of 6 m/s:
\[
\text{Height after 5 seconds} = \text{Rate} \times \text{Time} = 6 \text{ m/s} \times 5 \text{ s} = 30 \text{ m}
\]
However, according to the problem, the drone is at a height of 40 m after 5 seconds, which implies there might be a different starting height or the rate of change is not uniform.
Assuming the drone starts from ground level, we can recalculate based on the increase and compare to what we observe.
In 5 seconds at the rate of 6 m/s, you'd find the height is 30 meters, but since it is provided that the height is 40 meters, we can understand that:
- The drone may have started from a height of 10 meters (40 m - 30 m = 10 m).
Therefore, the rate of change is consistent, and it is **6 meters per second**.
The drone rises 18 meters every 3 seconds. We can calculate the rate of change (or speed) as follows:
\[
\text{Rate of change} = \frac{\text{Height increase}}{\text{Time interval}} = \frac{18 \text{ m}}{3 \text{ s}} = 6 \text{ m/s}
\]
Now, we also want to verify that the drone being at a height of 40 meters after 5 seconds fits within this rate of change.
1. Calculate the total height the drone would have after 5 seconds at a rate of 6 m/s:
\[
\text{Height after 5 seconds} = \text{Rate} \times \text{Time} = 6 \text{ m/s} \times 5 \text{ s} = 30 \text{ m}
\]
However, according to the problem, the drone is at a height of 40 m after 5 seconds, which implies there might be a different starting height or the rate of change is not uniform.
Assuming the drone starts from ground level, we can recalculate based on the increase and compare to what we observe.
In 5 seconds at the rate of 6 m/s, you'd find the height is 30 meters, but since it is provided that the height is 40 meters, we can understand that:
- The drone may have started from a height of 10 meters (40 m - 30 m = 10 m).
Therefore, the rate of change is consistent, and it is **6 meters per second**.