The physics of pulling in a swimmer while white water rafting

 One of my family’s favorite things to do is go white water rafting. One of the most important things you need to know is how to pull someone back into the boat if they fall out. The technique that is used for this begins with dunking the swimmer under the water by their life jacket straps then leaning back onto the boat to pull them up on top of you. The physics concept this mechanism relies on is the buoyant force. When the swimmer is pushed all the way under the water, more volume is displaced which increases the buoyant force. Since the buoyant force can be written as Fb= ρfluidVg, the greater the volume displaced, so the more of the swimmer’s volume that is submerged, the greater the buoyant force is which allows for the rescuer to apply a smaller force and still pull the swimmer out of the water

The best thing about this technique is that it allows for smaller rescuers to pull up bigger swimmers. In this instance, if the swimmer starts at rest and ends at rest, we can approximate the amount of force a rescuer needs to exert to pull a swimmer up enough to pull them up out of the water. 

If this is the system:

The force the rescuer needs to apply is:

Once the swimmer has been pulled out of the water, the second part of the mechanism, where the rescuer leans back on the boat and rotates about their feet, pulls the swimmer over the horizontal distance of the tube on the boat. This portion of the mechanism relies on the torque the rescuer generated by rotating backward, pulling their center of mass from directly over their feet to a more horizontal position. Since the torque is not constant, the angular acceleration is not constant, and thus the amount of work done by the rescuer can be approximated by finding the area under the graph of the torque as the angle changes. 

In this portion of the mechanism, you can find what speed the rescuer and the swimmer hit the surface of the boat by examining the energy:

In reality, these two motions are completed at almost the same time, but by breaking them down into components, this mechanism can be approximated by the physics we have learned in this class.