A 80.0 kg diver steps off a diving board and drops straight down into the water. The water provides an upward average net force 1320 N. If the diver comes to rest 5.1 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 the forces acting on the diver and use the principles of physics.
Let's analyze the problem step by step:
1. Determine the weight of the diver:
The weight of an object can be calculated using the formula: weight = mass * gravitational acceleration.
Given that the mass of the diver is 80.0 kg, and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight as:
weight = 80.0 kg * 9.8 m/s^2 = 784 N.
2. Calculate the net force acting on the diver:
The net force is the vector sum of all the forces acting on an object.
In this case, there are two forces acting on the diver: weight (acting downwards) and the upward net force provided by the water.
Since the diver comes to rest, the net force acting on the diver is zero.
Therefore, we can write the equation as:
upward net force - weight = 0.
Applying this to the problem, we have:
1320 N - 784 N = 0.
This gives us the upward net force provided by the water:
upward net force = 1320 N.
3. Calculate the distance traveled by the diver until coming to rest:
We can use the work-energy principle to determine the distance.
The work done by the upward net force is equal to the change in potential energy of the diver.
The potential energy of an object near the Earth's surface can be calculated using the formula: potential energy = mass * gravitational acceleration * height.
In this case, the mass of the diver is 80.0 kg, the gravitational acceleration is approximately 9.8 m/s^2, and the height is 5.1 m.
The work done by the upward net force is equal to the negative change in potential energy, so we can write:
work = -change in potential energy.
Using the formula for potential energy, we can calculate the change in potential energy as:
change in potential energy = mass * gravitational acceleration * change in height.
Substituting the given values, we have:
change in potential energy = 80.0 kg * 9.8 m/s^2 * 5.1 m = 4039.2 J.
Therefore, the work done by the upward net force is:
work = -4039.2 J.
4. Determine the distance traveled by the diver:
Since work is equal to force multiplied by distance (work = force * distance), and the work done by the upward net force is equal to -4039.2 J, we can rewrite the equation as:
-4039.2 J = 1320 N * distance.
Solving for distance, we get:
distance = -4039.2 J / 1320 N = -3.061 m.
The negative sign indicates that the distance traveled is in the downward direction.
5. Calculate the total distance between the diving board and the diver's stopping point underwater:
The total distance is the sum of the initial height of the diver and the distance traveled downward.
Given that the diver comes to rest 5.1 m below the water's surface, the total distance would be:
total distance = 5.1 m + (-3.061 m) ≈ 1.038 m.
Therefore, the total distance between the diving board and the diver's stopping point underwater is approximately 1.038 meters.