Melissa is flying a drone. She is controlling the drone so that it descends at a constant rate. After descending for 6 seconds, the drone is 434 meters high. After 11 seconds, the drone is 404 meters high.
Choose the statement that best describes how the time and the altitude of the drone are related. Then fill in the blank.
As time increases, the altitude of the drone decreases.
As time increases, the altitude of the drone increases.
(b)What was the altitude of the drone when it started its descent?
To understand the relation between time and altitude, let's calculate the rate of descent. We have two data points:
1. After 6 seconds, the altitude is 434 meters.
2. After 11 seconds, the altitude is 404 meters.
The difference in time is \( 11 - 6 = 5 \) seconds.
The difference in altitude is \( 434 - 404 = 30 \) meters.
To find the rate of descent per second, we divide the difference in altitude by the difference in time:
Rate of descent = \( \frac{30 \text{ meters}}{5 \text{ seconds}} = 6 \text{ meters per second} \).
This means the drone is descending at a rate of 6 meters every second. Hence, as time increases, the altitude of the drone decreases.
(a) The correct statement is: As time increases, the altitude of the drone decreases.
Now, let's find the altitude of the drone when it started its descent.
We already know that in 6 seconds, the drone descends by \( 6 \text{ seconds} \times 6 \text{ meters/second} = 36 \text{ meters} \).
Since the drone was at 434 meters after 6 seconds of descent, we add the 36 meters it descended to find the starting altitude:
Starting altitude = \( 434 \text{ meters} + 36 \text{ meters} = 470 \text{ meters} \).
(b) The altitude of the drone when it started its descent was 470 meters.