Final answer:
To stop the boat and its riders with a combined mass of 800 kg drifting at 1.8 m/s, Sam must do work equal to the kinetic energy of the boat, which is calculated as 1296 Joules.
Step-by-step explanation:
To calculate the amount of work Sam does to stop a boat with riders having a total mass of 800 kg that is drifting at 1.8 m/s, we need to use the concept of kinetic energy. Work is defined as the energy transferred to or from an object via the application of force along a displacement. In this instance, Sam is applying a force over a distance to bring the boat to a stop. Since no distance or time is given, we cannot calculate the work done using force and displacement directly. However, work can also be equal to the change in kinetic energy, and to stop the boat, Sam must do work equal to the negative of the boat's initial kinetic energy.
The kinetic energy (KE) of the boat and its riders is given by the formula KE = (1/2)mv², where m is the mass and v is the velocity. So, KE = (1/2)(800 kg)(1.8 m/s)² = 1296 J. Therefore, Sam must do 1296 Joules of work to bring the boat to a stop.