Final answer:
Two water-skiers with a combined mass of 109 kg, being towed with a force of 290 N, will accelerate at a rate of approximately 2.66 m/s².
Step-by-step explanation:
The question concerns the rate of acceleration of two water-skiers when towed behind a boat with a specified force exerted by the rope. We can calculate this using Newton's second law, which states that the acceleration of an object is equal to the net force acting upon it divided by the object's mass (a = F/m). Given that the combined mass of the skiers is 48 kg + 61 kg = 109 kg and the force provided by the rope is 290 N, we have:
a = F/m = 290 N / 109 kg ≈ 2.66 m/s2
This calculation yields the rate of acceleration for the two skiers. In terms of the maximum length of rope for waterskiing, the question does not provide enough details to address this point directly. However, typically a ropes' force constant and the skiers' weight would factor into any changes to the rope length, assuming an increase in length, which affects tension and elasticity.