# Finding distance with the conservation of energy equation

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In summary, the conversation discusses a problem involving a thrown baseball with given initial conditions. The initial kinetic energy of the ball is found correctly in part (a). In part (b), there is a discussion on using conservation of energy to find the maximum height reached by the ball, with a mistake made in the calculation of the final potential energy. After correcting the error, the correct answer is obtained.
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## Homework Statement

3. A baseball (m = 0.150 kg) is thrown with an initial speed of 30.0 m/s at an angle of 37.0 degrees from the horizontal at y = 0 m. (a) Find the initial KE of the ball. (b) Use conservation of energy (not kinematic equations) to find the maximum height reached by the ball. (Hint: Does the ball have any velocity at its maximum height?)

## Homework Equations

KEf + Uf = KEi + Ui
(.5)mvf² + mgyf = (.5)mvi² + mgyi

## The Attempt at a Solution

(a) Part a I got the correct answer, but can you tell me if I did it the correct way. I did (.5)(0.15)(30)² = 67.5J

(b) What I tried was using KEf + Uf = KEi + Ui . For the velocity at the top I accounted for the angle and got that the velocity in the x direction was 24.0m/s So I did:

(.5)(0.15)(24.0)² + (.5)(9.8)y = 67.5 (from part a) + (0.15)(9.8)(0)

Solving for y I get 4.96m, but that is not the correct answer. I'm not sure if I am doing it the wrong way or if I made some error somewhere, so any help would be appreciated.

Thanks

You did 'a' correctly.

Oh wow, thanks a lot. I changed the m in Uf to .15 and then got 16.6m which is the correct answer. It's unfortunate I've spent all this time on this problem due to this small error, though it's reassuring to know I was doing it the right way at least. Thanks again!

## 1. How is distance calculated using the conservation of energy equation?

The conservation of energy equation states that the initial energy of a system is equal to the final energy of the system. In the case of finding distance, the initial energy is equal to the potential energy (mgh) and the final energy is equal to the kinetic energy (1/2mv^2). By setting these two equations equal to each other and solving for distance (h), we can calculate the distance traveled by an object.

## 2. Can the conservation of energy equation be used for all types of motion?

Yes, the conservation of energy equation can be used for all types of motion. This equation applies to both linear and rotational motion, as long as there are no external forces acting on the system. In other words, the total energy of the system remains constant throughout the motion.

## 3. How does the mass of an object affect the distance it travels using the conservation of energy equation?

The mass of an object does not directly affect the distance it travels using the conservation of energy equation. However, the mass does affect the initial and final energies of the system. A heavier object will have a greater initial potential energy and a greater final kinetic energy, resulting in a larger distance traveled.

## 4. Can the conservation of energy equation be used to find the distance of an object in the presence of external forces?

No, the conservation of energy equation only applies to systems with no external forces acting on them. In the presence of external forces, the total energy of the system is not constant and the equation cannot be used to find the distance traveled.

## 5. How accurate is the conservation of energy equation in real-life situations?

The conservation of energy equation is a fundamental principle in physics and is highly accurate in real-life situations. However, it is important to note that this equation assumes ideal conditions and does not take into account factors such as air resistance, friction, and other external forces that may affect the motion of an object. Therefore, the calculated distance may differ slightly from the actual distance traveled in real-life situations.

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