A 69 kg swimmer free-falls off a 10.0 m diving platform. The diver comes to a stop 2.7 m below the water's surface. What is the magnitude of the force exerted by the water on the swimmer. (assume a positive direction is up)

I calculated the force on the diver before they hit the water was 676.2 N, however, I am not sure how to calculate the resistance given from the water. Thank you.

To calculate the magnitude of the force exerted by the water on the swimmer, we can use the concept of work and energy.

First, let's calculate the potential energy of the swimmer before they hit the water's surface. We can use the formula:

Potential Energy = mass * gravity * height

Given that the mass of the swimmer is 69 kg, the acceleration due to gravity is approximately 9.8 m/s², and the height is 10.0 m, we can calculate the potential energy:

Potential Energy = 69 kg * 9.8 m/s² * 10.0 m
Potential Energy = 6762 J

Now, let's calculate the potential energy of the swimmer when they come to a stop 2.7 m below the water's surface:

Potential Energy = mass * gravity * depth

Given that the depth is 2.7 m, we can calculate the potential energy:

Potential Energy = 69 kg * 9.8 m/s² * 2.7 m
Potential Energy = 1767.06 J

To find the force exerted by the water, we can subtract the final potential energy from the initial potential energy. This difference is the work done by the water to bring the swimmer to a stop:

Work = Initial Potential Energy - Final Potential Energy
Work = 6762 J - 1767.06 J
Work = 4994.94 J

By definition, work is equal to the force exerted on an object multiplied by the distance over which the force is applied. In this case, we can assume the force is constant, as it is the resistance of the water. The distance is the depth of the water (2.7 m). Therefore, we can rewrite the equation as:

Work = Force exerted by water * distance

Solving for the force, we have:

Force exerted by water = Work / distance
Force exerted by water = 4994.94 J / 2.7 m
Force exerted by water ≈ 1849.24 N

Therefore, the magnitude of the force exerted by the water on the swimmer is approximately 1849.24 N.