A scuba diver makes a slow descent into the depths of the ocean. His vertical position with respect to a boat on the surface changes several times. He makes the first stop 9.0 metres from the boat, but has a problem with equalizing the pressure, so he ascends 3.0 metres and then continues descending for another 12.0 metres to the second stop. From there, he ascends four metres and then descends for 18.0 metres, ascends again for seven metres and descends again for 24.0 metres, where he makes a stop, waiting for his buddy. What is his distance to the boat?
Let’s call this distance that we’re solving for, 𝑑, and we can begin by drawing a sketch of the situation. We have a scuba diver under water making a descend directly beneath a boat. The diver descends and ascends several different times for several different distances. And we want to figure out at the end of all the diver’s motion, what is the diver’s vertical distance 𝑑 from the boat?
In this problem, let’s consider descending motion, that is motion down into the water, to be motion in the positive direction. This means that our answer 𝑑 will be positive. Now, let’s recollect all the descending and ascending the diver did. First, the diver moved down 9.0 metres, then up 3.0 metres, then down 12.0 metres, then up four metres, then down 18.0 metres, up seven metres, and finally down 24.0 metres.
To solve for the diver’s final distance 𝑑 below the boat, we add together each one of these lags of the journey, being careful to obey our sign convention that motion down is positive and ascending motion is negative. When we add all these journey segments together, we get a final distance 𝑑 of 49 metres. That’s how far the diver ends up from the boat.