A 51.0 kg diver steps off a diving board and drops straight down into the water. The water provides an upward average net force 1370 N. If the diver comes to rest 4.6 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 motion of the diver.
We can use the concept of work and energy to determine the total distance. When the diver drops, the work done by the water's upward force (1370 N) is converted into gravitational potential energy. The work done by a force is equal to the product of the force and the displacement in the direction of the force.
Work = Force x Displacement
Since the water's force is acting in the upward direction and the diver is dropping down, the displacement is negative. Therefore, the work done by the water is:
Work = (1370 N) x (-4.6 m) = -6310 J
The work done by the water is equal to the change in the diver's gravitational potential energy (PE). The change in potential energy is given by the formula:
PE = mgh
Where m is the mass of the diver (51.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height or depth (4.6 m). Substituting the values:
-6310 J = (51.0 kg) x (9.8 m/s^2) x (4.6 m)
Now, we can solve for the depth or height (h):
h = (-6310 J) / [(51.0 kg) x (9.8 m/s^2)]
h ≈ -12.6 m
The negative sign indicates that the diver's stopping point is below the diving board. However, distance cannot be negative. To find the total distance, we take the absolute value of the depth:
Total Distance = |h| = |-12.6 m| = 12.6 m
Therefore, the total distance between the diving board and the diver's stopping point underwater is 12.6 meters.