Final answer:
The water-skier experiences a vertical acceleration of 2.995 m/s² on his return to the water surface.
Step-by-step explanation:
To determine the vertical acceleration that the water-skier experiences on his return to the water surface, we need to consider the net force acting on the skier. Since the air resistance can be ignored, the net force is equal to the force exerted by the boat minus the weight of the skier. The weight can be calculated using the formula: weight = mass x gravity, where the mass of the skier is 68 kg and the acceleration due to gravity is 9.8 m/s². Thus, the weight is 68 kg x 9.8 m/s² = 666.4 N.
The net force is the force exerted by the boat (870 N) minus the weight (666.4 N), which gives us a net force of 870 N - 666.4 N = 203.6 N. This net force is responsible for the skier's vertical acceleration.
Using Newton's second law, which states that F = ma, where F is the net force, m is the mass, and a is the acceleration, we can rearrange the formula to solve for acceleration: a = F / m. Plugging in the values, we get a = 203.6 N / 68 kg = 2.995 m/s².
Therefore, the vertical acceleration that the water-skier experiences on his return to the water surface is approximately 2.995 m/s².