Sink or Float? Sailors Dive Training Riddle

Sailors Dive Training

A couple years ago, when my kids were in elementary school, I coached their school’s “Sink or Float” team for the Science Olympiad. The objective of the Sink or Float competition was straightforward: Students must demonstrate their ability to determine which objects will sink and which will float. The team that does this correctly in the most number of situations wins the event. Although not part of the official event, I used the Sailors Dive Training Riddle to get the kids to really think about the factors that determine whether something will sink or float–weight, volume, density, displacement, buoyancy, etc.

It’s a fun riddle. Like most riddles, it’s rather tricky, until you think about it just right. Then, all of a sudden, it becomes obvious. Give it a try!

Sailors Dive Training

As part of their normal training, a group of student sailors is learning to scuba dive. For today’s training activity, the sailors are learning how to put on diving gear when already underwater. The exercise works as follows.

1. A sailor and an instructor get into a rowboat in a large swimming pool along with two complete sets of scuba diving gear (e.g., tanks, fins, masks, weight belts, etc.)
2. They row the boat to the deep end of the pool. Where they drop one complete set of diving gear overboard, allowing it to sink to the bottom of the pool.
3. The instructor then dons the other set of gear, jumps into the water and sits at the bottom of the pool next to the submerged gear.
4. Once the instructor is at the bottom, the student must then jump overboard, swim to the bottom, and don the gear that is waiting at the bottom of the pool. The instructor is there as a safety precaution and to observe the student.
5. Once the student has demonstrated to the instructor that all the gear has been put on and is operating correctly, he or she surfaces, removes all the gear and places it back in the boat, then swims back down to the bottom of the pool and gives the instructor a “thumbs up” sign.

So, that’s the training.  Now for the riddle…

Sink or Float

Suppose, at the end of each step above, we were to measure (very accurately) the average depth of water in the pool. At the end of each of steps 2 through 5, how does the average depth compare to that of the previous step? For example, how does the depth at the end of step 2 compare to the depth at the end of step 1? How does step 3 compare to step 2? And so on. In each case, the average depth could be higher, lower, or the same as that of the previous step.

Leave your answers as a comment below. For extra credit, explain your reasoning.

Good luck!