A 47.6-kg diver steps off a 10.82 m high diving board and drops straight down into the water. If the diver comes to rest 5.3 m below the surface of the water, determine the average resistance force exerted on the diver by the water.
What is the total displacement of the diver?What is the average resistance force exerted on the diver by the water.
To determine the total displacement of the diver, we need to find the vertical distance the diver traveled from the top of the diving board to the bottom of the body of water. Since the diver starts 10.82 m above the water and comes to rest 5.3 m below the surface, the total displacement can be calculated as:
Total displacement = 10.82 m + 5.3 m
Total displacement = 16.12 m
So, the total displacement of the diver is 16.12 m.
To calculate the average resistance force exerted on the diver by the water, we can use the work-energy principle. According to this principle, the work done on an object is equal to its change in kinetic energy. Since the diver comes to rest, the work done on the diver by the resistance force is equal to the initial kinetic energy of the diver.
The initial kinetic energy of the diver can be calculated using the formula:
Initial kinetic energy = 0.5 * mass * velocity^2
Since the diver dropped straight down, the initial velocity of the diver can be calculated using the formula:
Initial velocity = sqrt(2 * acceleration * displacement)
Where acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2, and displacement is the total displacement of the diver, which is 16.12 m. Substituting these values into the formula, we can calculate the initial velocity:
Initial velocity = sqrt(2 * 9.8 m/s^2 * 16.12 m)
Initial velocity ≈ 18.99 m/s
Now, we can calculate the initial kinetic energy:
Initial kinetic energy = 0.5 * 47.6 kg * (18.99 m/s)^2
Initial kinetic energy ≈ 8561.52 J
Therefore, the average resistance force exerted on the diver by the water is equal to the initial kinetic energy, which is approximately 8561.52 J.
To determine the total displacement of the diver, we need to calculate the distance the diver travels from the diving board to the water's surface plus the distance the diver travels underwater.
First, calculate the distance traveled from the diving board to the water's surface:
Distance = 10.82 m
Next, calculate the distance traveled underwater:
Distance = 5.3 m
To find the total displacement of the diver, add the two distances together:
Total displacement = 10.82 m + 5.3 m
Total displacement = 16.12 m
Next, let's calculate the average resistance force exerted on the diver by the water.
The average resistance force can be calculated using the work-energy principle. The work done by the resistance force equals the change in the diver's kinetic energy.
The initial kinetic energy of the diver is zero since the diver begins at rest. The final kinetic energy of the diver is also zero since the diver comes to rest. Therefore, the change in kinetic energy is zero.
Work done by the resistance force = change in kinetic energy
Since the work done is equal to the force multiplied by the distance, we can write:
Force x 16.12 m = 0
Therefore, the average resistance force exerted on the diver by the water is zero.