Question

mai is flying a drone. she is controlling the drone so that it ascends at a constant rate. after ascending for 7 seconds, the drone is 138 meters high. after 28 seconds, the drone is 285 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.

○ as time increases, the altitude of the drone decreases.
the altitude of the drone decreases at a rate of \\(\square\\) meters per second

○ as time increases, the altitude of the drone increases.
the altitude of the drone increases at a rate of \\(\square\\) meters per second.

(b) what was the altitude of the drone when it started its ascent?
\\(\square\\) meters

Explanation:

Step1: Determine relationship direction

The drone ascends, so altitude increases with time. Select the second statement.

Step2: Calculate ascent rate

Find the difference in altitude and time:
$\text{Rate} = \frac{285 - 138}{28 - 7} = \frac{147}{21} = 7$ meters per second

Step3: Find initial altitude

Use linear equation $h = rt + h_0$. Plug $t=7$, $h=138$, $r=7$:
$138 = 7\times7 + h_0$
$138 = 49 + h_0$
$h_0 = 138 - 49 = 89$

Answer:

(a) As time increases, the altitude of the drone increases.
The altitude of the drone increases at a rate of 7 meters per second.
(b) 89 meters