Final answer:
When driving a boat while towing a waterskier, the rate of acceleration for the skiers can be calculated using Newton's second law of motion. In this case, the net force exerted by the rope on the skiers is 290 N, and the combined mass of the skiers is 109 kg. The rate of acceleration is 2.66 m/s^2.
Step-by-step explanation:
When driving a boat while towing a waterskier, you must consider the forces acting on the skier. As the boat accelerates, the force exerted by the rope on the skiers causes them to accelerate as well.
Using Newton's second law of motion, which states that force equals mass times acceleration (F = ma), we can calculate the rate of acceleration for the skiers.
In this case, the net force exerted by the rope on the skiers is 290 N. The combined mass of the skiers is 48 kg + 61 kg = 109 kg.
Therefore, the rate of acceleration for the skiers can be calculated using the formula a = F/m, where a is the acceleration, F is the force, and m is the mass.
Plugging in the values, we have a = 290 N / 109 kg = 2.66 m/s^2.