A scuba diver was at a depth of 15 meters below the surface when she saw something interesting about 10 meters lower. She made the descent in 10.1 seconds. Interpret the quotient to describe the rate of change in the diver’s depth. Give your answer to the nearest hundredth.

Question

is the answer positive or negative

Answer 1

To find the rate of change in the diver's depth, we first need to determine the total change in depth and then divide that by the time taken for the descent.

1. Initial depth of the diver: -15 meters (below the surface)
2. Final depth after descending further: -15 meters - 10 meters = -25 meters (below the surface)
3. Change in depth: \[ \Delta d = \text{Final depth} - \text{Initial depth} = -25 - (-15) = -25 + 15 = -10 \text{ meters} \]
4. Time taken: 10.1 seconds
5. Rate of change of depth: \[ \text{Rate} = \frac{\Delta d}{\text{Time}} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}} \approx -0.9901 \text{ m/s} \]

Rounding to the nearest hundredth, the rate of change in the diver’s depth is approximately -0.99 m/s.

Since the rate is negative, this indicates that the diver is descending, which is consistent with the situation described.