# Impulse-Momentum Theorem and diving board

• chops369
In summary, the problem involves an 82 kg man dropping from rest on a diving board 3m above the water's surface. After reaching the water, he comes to rest in 0.55 s. By using the equation x=at^2/2, the time it takes for the diver to reach the water can be calculated. Then, using the equation v=x/t, the velocity of the diver just before hitting the water can be found. This velocity is then used in the equation F=m(Vf-Vi)/t to calculate the force exerted by the water on the diver, which is approximately 820 N. However, it should be noted that this solution may not be entirely accurate as it does not take into
chops369

## Homework Statement

An 82 kg man drops from rest on a diving board 3m above the surface of the water and comes to rest 0.55 s after reaching the water. What force does the water exert on him?

## Homework Equations

F = mVf - mVi / t

## The Attempt at a Solution

I have no idea where to begin since I don't know the diver's velocity. Could I possibly use V = d/t?

EDIT: Ok, so I used V = d/t and got 5.5 m/s for the velocity. Then I used F = mVf - mVi / t, and got 820 N. Is this correct?

I'm not saying that I'm in any way a physics expert or anything but;

What you calculated as the velocity was 3m/0.55s --> which is not at all the velocity of the diver just before he hits the water. I made a quick attempt at this problem, and I would instead use the relationship: x=at2/2, since the acceleration is constant. From this you can find the time it takes for the diver to hit the water--also knowing that x=vt, and therefore v=x/t, you can find the velocity of the diver just before he hits the water, which is also the initial velocity in (mVf-mVi)/t.

The Impulse-Momentum Theorem is a fundamental principle in physics that states that the change in momentum of an object is equal to the impulse applied to it. In the case of the 82 kg man on the diving board, the impulse is caused by the gravitational force acting on the man as he falls and the force exerted by the water as he enters it.

To calculate the force exerted by the water on the man, we can use the Impulse-Momentum Theorem equation F = mΔv / Δt, where F is the force, m is the mass of the man, Δv is the change in velocity, and Δt is the time interval.

In this case, we can use the given information to calculate the change in velocity (Δv). Since the man starts from rest and comes to rest after 0.55 seconds, we can calculate his final velocity (Vf) using the equation Vf = d / t, where d is the height of the diving board (3m) and t is the time interval (0.55s). This gives us a final velocity of 5.45 m/s.

Now, we can plug this value into the Impulse-Momentum Theorem equation along with the mass and time interval given to calculate the force exerted by the water. This gives us F = (82 kg)(5.45 m/s) / 0.55 s = 810 N.

Therefore, the water exerts a force of 810 N on the man as he enters it from the diving board. It is important to note that this is an average force and may vary during the dive due to factors such as the man's body position and the resistance of the water.

## 1. What is the Impulse-Momentum Theorem?

The Impulse-Momentum Theorem is a physical law that states that the change in momentum of an object is equal to the impulse applied to it. This means that the force applied to an object over a certain amount of time will result in a change in its momentum.

## 2. How does the Impulse-Momentum Theorem apply to a diving board?

In the context of a diving board, the Impulse-Momentum Theorem can be used to explain how the force of the diver's jump affects their momentum. The force of the jump, combined with the elasticity of the diving board, will determine the height and speed of the diver as they leave the board.

## 3. Can the Impulse-Momentum Theorem be used to calculate the height of a dive?

Yes, the Impulse-Momentum Theorem can be used to calculate the height of a dive. By knowing the force applied by the diver and the time it takes for them to leave the board, their change in momentum can be calculated. This can then be used to determine the height they will reach based on their initial momentum and gravitational acceleration.

## 4. How is the Impulse-Momentum Theorem related to Newton's Laws of Motion?

The Impulse-Momentum Theorem is based on Newton's Second Law of Motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. The Impulse-Momentum Theorem expands on this concept by incorporating the time over which the force is applied, as well as the initial and final momentum of the object.

## 5. How does the elasticity of the diving board affect the application of the Impulse-Momentum Theorem?

The elasticity of the diving board plays a crucial role in the application of the Impulse-Momentum Theorem. The more elastic the board is, the greater the force it will apply to the diver, resulting in a higher change in momentum and therefore a higher dive. However, if the board is too rigid or not elastic enough, the force may not be evenly distributed and could result in an unpredictable jump for the diver.

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