A 62.9 kg diver steps off a diving board and drops straight down into the water. The water provides an upward average net force 1350 N. 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?
To find the total distance between the diving board and the diver's stopping point underwater, we need to consider the two parts of the motion: the distance traveled while the diver is in contact with the water and the distance traveled after the diver reaches the water's surface.
1. Distance traveled while in contact with water:
When the diver is in contact with the water, the net force acting on the diver is equal to the weight of the diver minus the buoyant force provided by the water. Since the diver comes to rest, the upward buoyant force must be equal to the downward weight of the diver.
The weight of the diver can be calculated using the formula: weight = mass × gravity.
weight = 62.9 kg × 9.8 m/s^2 = 616.42 N.
Since the water provides an upward net force of 1350 N, the buoyant force is 1350 N.
Therefore, the distance traveled while in contact with the water can be calculated using the work-energy principle:
work done by the buoyant force = force × distance = 1350 N × distance.
This work done by the buoyant force should be equal to the potential energy gained by the diver:
potential energy = weight × distance = 616.42 N × distance.
Setting these two equations equal, we can solve for the distance traveled while in contact with the water:
1350 N × distance = 616.42 N × distance.
This equation gives us the distance traveled while in contact with the water.
2. Distance traveled after reaching the water's surface:
Once the diver comes to rest underwater, the net force acting on the diver becomes zero. Therefore, the only force acting on the diver is the upward buoyant force, which is equal to the weight of the diver. The buoyant force can be calculated using the formula: buoyant force = density × volume × gravity, but since the density and the volume are unknown, we need additional information to calculate this distance.
To find the total distance traveled by the diver, we need to calculate the distance while in contact with the water and then add it to the distance traveled after reaching the water's surface.