How Far Does the Diver Travel from Board to Stopping Point Underwater?

[jojo42586]

i think i got a start on this one, but I'm not quite sure where to go!

problem: a 53.5 kg diver steps off a diving board and drops straight down into the water. the water provides an average net force of resistance of 1552 N to the diver's fall. the acceleration of gravity is 9.81 m/s^2. If the diver comes to rest 4.3 m below the water's surface, what is the total distance between the diving board and the diver's stopping point underwater? answer in units of m.

so so far, i have found the force of gravity that is working on the diver to be 524.835 N. I know that net work equals the net force times displacement, but i can't find the displacement, because the only thing that I've really solved for is the net force. help!

 

[Astronuc]

The diver accelerates to some velocity when he hits the water. Then he begins to decelerate due to drag of the water. If you assume that the density of the diver is approximately the same as water, then the bouyancy in the water offsets the force of gravity, so one only need consider the drag in the water.

The average force of the water resistance is 1552 m, almost 3 times the force of gravity on the diver.

Think of how force, acceleration and distance relate.

 

[wais]

First of all, good job on starting to solve the problem! Let's break down the steps to find the total distance between the diving board and the diver's stopping point underwater.

1. Find the displacement of the diver: We know that the diver starts at the diving board and comes to rest 4.3 m below the water's surface. This means that the displacement is 4.3 m.

2. Find the net work done on the diver: As you mentioned, net work equals the net force times displacement. We have the net force of resistance (1552 N) and the displacement (4.3 m), so we can calculate the net work done on the diver.

3. Find the work done by gravity: We also need to consider the work done by gravity on the diver. This can be found by using the formula W = mgh, where m is the mass of the diver (53.5 kg), g is the acceleration due to gravity (9.81 m/s^2), and h is the height the diver falls (4.3 m).

4. Use the work-energy theorem: The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. In this case, the kinetic energy of the diver at the start is zero (since they are standing still on the diving board), and at the stopping point underwater, the kinetic energy is also zero (since they have come to rest). This means that the net work done on the diver is equal to the work done by gravity.

5. Set up an equation: We can now set up an equation using the net work done on the diver (found in step 2) and the work done by gravity (found in step 3). This will give us an equation with only one variable, which we can solve for.

6. Solve for the total distance: Once we have solved the equation and found the value of the variable, we can plug it back into the displacement formula (step 1) to find the total distance between the diving board and the diver's stopping point underwater.

I hope this helps guide you in the right direction and gives you a clearer understanding of how to approach the problem. Keep in mind that in physics, it's important to always consider all the forces and energies involved in a situation. Good luck!