Kaitlin is flying a drone. She is controlling the drone so that it descends at a constant rate. After descending for 14 seconds, the drone is 224 meters high. After 27 seconds, the drone is 107 meters high.
(a)Choose the statement that best describes how the time and the altitude of the drone are related. Then fill in the blank.
Statement 1: As time increases, the altitude of the drone decreases. The altitude of the drone decreases at a rate of ___ meters per second.
Statement 2: As time increases, the altitude of the drone increases. The altitude of the drone increases at a rate of ___ meters per second.
(b)What was the altitude of the drone when it started its descent?was the altitude of the drone when it started its descent? ___ meters
(a) Statement 1: As time increases, the altitude of the drone decreases. The altitude of the drone decreases at a rate of \(\frac{224-107}{14-27}\) meters per second.
Calculating the rate of descent, \(\frac{224-107}{14-27} = \frac{117}{-13} = -9\) meters per second
Therefore, the altitude of the drone decreases at a rate of 9 meters per second.
(b) To find the altitude of the drone when it started its descent, we can use the rate of descent of 9 meters per second and the information given.
Let h be the altitude when the drone started its descent.
Using the rate formula \(h = vt + c\), where V is the rate of descent, t is the time elapsed, and c is the initial altitude (unknown).
When t = 14 seconds, h = 224 meters
\(224 = 9(14) + c\)
\(224 = 126 + c\)
\(c = 98\)
Therefore, the altitude of the drone when it started its descent was 98 meters.