Final answer:
The acceleration rate at which the two skiers will accelerate when towed by a boat exerting a force of 290 N is 2.66 meters per second squared, calculated using Newton's second law of motion.
Step-by-step explanation:
To solve for the acceleration rate of the two water-skiers being towed behind the same boat, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass ($ F = ma $, where $ F $ is force, $ m $ is mass, and $ a $ is acceleration).
The combined mass of the skiers is $ 48 kg + 61 kg = 109 kg $. The net force given is 290 Newtons (N). Using Newton's second law, we have $ a = \frac{F}{m} $, where $ a $ is the acceleration, $ F $ is the net force, and $ m $ is the combined mass of the skiers.
Substituting the given values we get $ a = \frac{290 N}{109 kg} $ which equals approximately 2.66 meters per second squared ($ m/s^2 $). Therefore, the acceleration rate at which the skiers will accelerate is 2.66 $ m/s^2 $.