A 56.0 kg diver steps off a diving board and drops straight down into the water. The water provides an upward average net force 1310 N. If the diver comes to rest 4.1 m below the water's surface, what is the total distance between the diving board and the diver's stopping point underwater?

To find the total distance between the diving board and the diver's stopping point underwater, we need to consider both the distance traveled in the air and the distance traveled underwater.

First, let's calculate the distance traveled in the air. We can use the equation that relates distance, initial velocity, final velocity, and acceleration:

d_air = (v_final)^2 - (v_initial)^2 / (2 * a)

Since the diver drops straight down, the initial velocity in the air is 0 m/s. The final velocity in the air can be calculated using the formula:

v_final^2 = v_initial^2 + 2 * a * d_air

Here, a is the acceleration due to gravity, which is approximately 9.8 m/s^2. We can rearrange the equation to solve for v_final:

v_final = sqrt(v_initial^2 + 2 * a * d_air)

Since v_initial is 0 m/s, the equation simplifies to:

v_final = sqrt(2 * a * d_air)

Now, let's calculate the distance traveled underwater. We can use the equation:

d_underwater = (v_initial)^2 / (2 * a)

Since the diver comes to rest underwater, the final velocity is 0 m/s.

Now we have the distance in the air and underwater. The total distance traveled is the sum of these two distances:

total distance = d_air + d_underwater

Let's calculate the values:

a = 9.8 m/s^2
d_air = ?
v_initial = 0 m/s
v_final = ?
d_underwater = 4.1 m

To find d_air, we need to find v_final using the formula:

v_final = sqrt(2 * a * d_air)

1310 N is the net force acting on the diver in the water, which can be converted to weight using the equation:

Weight = mass * acceleration due to gravity

Weight = 56.0 kg * 9.8 m/s^2

Now we can substitute the weight into the equation for the net force in the water:

1310 N = (weight) - (buoyant force)

The buoyant force can be calculated using the equation:

buoyant force = volume * density * gravity

The volume can be given by:

volume = weight / density_water

where density_water is the density of water, which is approximately 1000 kg/m^3.

Now we can calculate the volume and then substitute it into the equation to find the buoyant force.

Finally, we can substitute the weight and buoyant force into the equation and solve for d_air:

1310 N = (weight) - (buoyant force)

Solve for weight:

(weight) = 56.0 kg * 9.8 m/s^2

Now, substitute the values into the equation and solve for d_air:

1310 N = (56.0 kg * 9.8 m/s^2) - (buoyant force)

Now that we have found d_air, we can calculate the total distance using:

total distance = d_air + d_underwater

Substitute the values and calculate the total distance traveled.