Question

1. a scuba diver is diving at a constant rate when her team on the surface requests a status update. she looks at her watch which says her elevation is 18 feet below sea level. 8 seconds later, her elevation is 20 feet below sea level.

a. at what rate is her elevation changing? use a signed number, and include the unit of measurement in your answer.
b. how many more seconds until she reaches her goal depth of 50 feet? explain or show your reasoning.
c. how many seconds before her team requested an update was the diver at the surface of the water? explain or show your reasoning.

Explanation:

Step1: Define variables for part a

Let initial elevation $e_1 = -18$ ft, final elevation $e_2 = -20$ ft, time $\Delta t = 8$ s.

Step2: Calculate elevation change rate

Rate = $\frac{\text{Change in elevation}}{\text{Change in time}}$
$\text{Rate} = \frac{e_2 - e_1}{\Delta t} = \frac{-20 - (-18)}{8} = \frac{-2}{8} = -\frac{1}{4}$ ft/s

Step3: Find time for part b

Remaining depth: $50 - 20 = 30$ ft. Time = $\frac{\text{Remaining depth}}{\text{Magnitude of rate}}$
$\text{Time} = \frac{30}{\frac{1}{4}} = 30 \times 4 = 120$ s

Step4: Calculate time for part c

Distance from surface to initial elevation: $18$ ft. Time = $\frac{\text{Distance}}{\text{Magnitude of rate}}$
$\text{Time} = \frac{18}{\frac{1}{4}} = 18 \times 4 = 72$ s

Answer:

a. $-\frac{1}{4}$ feet per second
b. 120 seconds
c. 72 seconds