Final answer:
By using the conservation of energy principle, the initial potential energy at the top of the water slide tube minus the energy lost to friction gives the kinetic energy at the bottom, from which the speed of the riders can be calculated.
Step-by-step explanation:
To calculate the speed of riders at the moment they reach the bottom of the slide, you can use the conservation of energy principle. The initial potential energy at the top of the slide is converted into kinetic energy and heat energy due to friction at the bottom of the slide. First, calculate the initial potential energy (PE), using PE = mgh, where m is mass, g is acceleration due to gravity, and h is the height. Then find the final kinetic energy (KE) at the bottom, knowing that the initial potential energy minus the energy lost to friction equals the kinetic energy at the bottom, KE = PE_initial - energy lost to friction. The kinetic energy is related to the speed (v) by the formula KE = 0.5 * m * v2. Rearrange this equation to solve for v, and plug in the numbers: KE = 0.5 * 270kg * v2, PE_initial = 270kg * 9.8m/s2 * 7.2m, and the energy lost to friction is 9,200J. Following these calculations: Calculate the total potential energy change: \( PE_initial - PE_final = mgh_initial - mgh_final = 270kg * 9.8m/s2 * (7.2m - 0.40m) \) Subtract the energy lost to friction: \( KE_bottom = (PE_initial - PE_final) - energy lost to friction \) Calculate the speed at the bottom using the kinetic energy formula: \( v = \sqrt{(2*KE_bottom)/m} \) By doing these calculations, you would find the speed of the riders at the bottom of the slide. The provided options can be checked by solving the equation using the conservation of energy principle.