Final answer:
The two water-skiers with a total mass of 109 kg, being towed by a boat that exerts a force of 290 N, will accelerate together at a rate of approximately 2.66 meters per second squared.
Step-by-step explanation:
The student asked about the acceleration rate of two water-skiers of different masses being towed by a boat. To find the acceleration, we will use Newton's second law, which states that Force (F) equals mass (m) times acceleration (a), or F=ma.
To find the combined acceleration for both skiers, we must first determine the total mass. The total mass (m) of the skiers is the sum of their individual masses, therefore, m_total = 48 kg + 61 kg = 109 kg.
With the total force applied being 290 N, and using the formula a = F/m_total, we can calculate:
a = 290 N / 109 kg.
The rate at which the skiers will accelerate based on the given force can now be calculated. Performing the division, a = 2.66 m/s^2 (rounded to two decimal places).
This means both water-skiers together will accelerate at a rate of approximately 2.66 meters per second squared, assuming all the force is used to only accelerate the skiers and no other external forces acting on them.