Final answer:
The two water-skiers, with a combined mass of 109 kg and experiencing a net force of 290 N, will accelerate at approximately 2.66 m/s² due to the force exerted by the towing rope.
Step-by-step explanation:
When two water-skiers with masses of 48 kg and 61 kg are towed behind a boat, the net force exerted by the boat through the towing rope is 290 N. To calculate the rate at which the skiers will accelerate, we use Newton's second law of motion, which states that the net force exerted on an object is equal to the mass of the object multiplied by its acceleration (F = ma). Here, the two skiers can be treated as a single system with a combined mass.
First, we find the total mass of the skiers by adding their individual masses:
- Mass of first skier = 48 kg
- Mass of second skier = 61 kg
- Total mass = 48 kg + 61 kg = 109 kg
Next, we apply Newton's second law to solve for the acceleration (a):
F = ma
290 N = 109 kg × a
To find 'a', divide both sides of the equation by the total mass:
a = × 290 N / 109 kg
Thus, the rate of acceleration for the skiers is:
a ≈ 2.66 m/s2