A 10 kg ball is thrown into the air. It is going 3.0 m/s when thrown. How much potential
energy will it have at the top?

To find the potential energy (\(PE\)) at the top of the ball's trajectory, we can use the principle of conservation of energy. According to this principle, the initial kinetic energy (\(KE\)) of the ball when it is thrown will be entirely converted into potential energy at the top of its trajectory, assuming no energy is lost to air resistance or other forces.

### Step 1: Calculate the initial kinetic energy.
The kinetic energy can be calculated using the formula:
\[
KE = \frac{1}{2} m v^2
\]
where:
- \(m\) is the mass of the ball (10 kg),
- \(v\) is the velocity when the ball is thrown (3.0 m/s).

\[
KE = \frac{1}{2} \times 10 \, \text{kg} \times (3.0 \, \text{m/s})^2 = \frac{1}{2} \times 10 \times 9 = 45 \, \text{J}
\]

So, the initial kinetic energy is 45 joules.

### Step 2: Determine the potential energy at the top.
At the top of the trajectory, the ball's velocity will be zero, meaning all the kinetic energy will have been converted into potential energy. Therefore, the potential energy at the top is equal to the initial kinetic energy:
\[
PE = 45 \, \text{J}
\]

So, the ball will have 45 joules of potential energy at the top of its trajectory.

Would you like more details or have any questions?

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Here are some related questions to consider:

1. How high will the ball go if its potential energy is 45 J?
2. What is the velocity of the ball when it hits the ground?
3. How would the potential energy change if the mass of the ball were different?
4. What happens to the potential energy if air resistance is considered?
5. How would the result change if the ball were thrown on another planet with different gravity?

**Tip:** Remember that energy conservation is a powerful tool in physics that allows you to solve many problems involving motion and forces.

A 10 kg ball is thrown into the air. It is going 3.0 m/s when thrown. How much potential energy will it have at the top?

Learn how to calculate the potential energy of a 10 kg ball thrown into the air at 3 m/s using energy conservation principles. This physics problem demonstrates the conversion of kinetic energy to potential energy, suitable for students in Grades 9-12.

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